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Chapters
2: Profit , Loss and Discount
3: Compound Interest
4: Expansions
5: Factorisation
6: Changing the subject of a formula
7: Linear Equations
8: Simultaneous Linear Equations
9: Indices
10: Logarithms
11: Triangles and their congruency
12: Isosceles Triangle
13: Inequalities in Triangles
14: Constructions of Triangles
15: Mid-point and Intercept Theorems
16: Similarity
17: Pythagoras Theorem
18: Rectilinear Figures
19: Quadrilaterals
20: Constructions of Quadrilaterals
21: Areas Theorems on Parallelograms
22: Statistics
23: Graphical Representation of Statistical Data
24: Perimeter and Area
25: Surface Areas and Volume of Solids
26: Trigonometrical Ratios
27: Trigonometrical Ratios of Standard Angles
28: Coordinate Geometry
![Frank solutions for Mathematics [English] Class 9 ICSE chapter 1 - Irrational Numbers - Shaalaa.com](/images/mathematics-english-class-9-icse_6:c41cc344f5174c64a036c55d113af73f.jpg "Frank solutions for Mathematics [English] Class 9 ICSE chapter 1 - Irrational Numbers")
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Solutions for Chapter 1: Irrational Numbers
Below listed, you can find solutions for Chapter 1 of CISCE Frank for Mathematics [English] Class 9 ICSE.
Frank solutions for Mathematics [English] Class 9 ICSE 1 Irrational Numbers Exercise 1.1
State if the following fraction has a terminating decimal
`(3)/(5)`
State if the following fraction has a terminating decimal
`(5)/(7)`
State if the following fraction has a terminating decimal
`(25)/(49)`
State if the following fraction has a terminating decimal
`(37)/(40)`
State if the following fraction has a terminating decimal
`(57)/(64)`
State if the following fraction has a terminating decimal.
`(59)/(75)`
State if the following fraction has a terminating decimal.
`(89)/(125)`
State if the following fraction has a terminating decimal.
`(125)/(213)`
State if the following fraction has a terminating decimal.
`(147)/(160)`
Express the following decimal as a rational number.
0.93
Express the following decimal as a rational number.
4.56
Express the following decimal as a rational number.
0.614
Express the following decimal as a rational number.
21.025
Convert the following fraction into a decimal :
`(3)/(5)`
Convert the following fraction into a decimal :
`(8)/(11)`
Convert the following fraction into a decimal :
`(-2)/(7)`
Convert the following fraction into a decimal :
`(12)/(21)`
Convert the following fraction into a decimal :
`(13)/(25)`
Convert the following fraction into a decimal :
`(2)/(3)`
Express the following decimal as a rational number.
0.7
Express the following decimal as a rational number.
0.35
Express the following decimal as a rational number.
0.89
Express the following decimal as a rational number.
0.057
Express the following decimal as a rational number.
0.763
Express the following decimal as a rational number.
2.67
Express the following decimal as a rational number.
4.6724
Express the following decimal as a rational number.
0.017
Express the following decimal as a rational number.
17.027
Insert a rational number between:
`(2)/(5) and (3)/(4)`
Insert a rational number between:
`(3)/(4) and (5)/(7)`
Insert a rational number between:
`(4)/(3) and (7)/(5)`
Insert a rational number between:
`(5)/(9) and (6)/(7)`
Insert a rational number between:
3 and 4
Insert a rational number between:
7.6 and 7.7
Insert a rational number between:
8 and 8.04
Insert a rational number between:
101 and 102
Insert three rational numbers between:
0 and 1
Insert three rational number between:
6 and 7
Insert three rational number between:
-3 and 3
Insert three rational number between:
-5 and -4
Insert five rational number between:
`(2)/(5) and (2)/(3)`
Insert five rational number between:
`-(3)/(4) and -(2)/(5)`
Find the greatest and the smallest rational number among the following.
`(6)/(7),(9)/(14) and (23)/(28)`
Find the greatest and the smallest rational number among the following.
`(-2)/(3) , (-7)/(9) and (-5)/(6)`
Arrange the following rational numbers in ascending order.
`(4)/(5),(6)/(7) and (7)/(10)`
Arrange the following rational numbers in ascending order.
`(-7)/(12), (-3)/(10) and (-2)/(5)`
Arrange the following rational numbers in ascending order.
`(10)/(9),(13)/(12) and (19)/(18)`
Arrange the following rational numbers in ascending order.
`(7)/(4), (-6)/(5) and (-5)/(2)`
Arrange the following rational numbers in descending order.
`(7)/(13),(8)/(15), and (3)/(5)`
Arrange the following rational numbers in descending order.
`(4)/(3), (-14)/(5) and (17)/(15)`
Arrange the following rational numbers in descending order.
`(-7)/(10), (-8)/(15) and (-11)/(30)`
Arrange the following rational numbers in descending order.
`(-3)/(8),(2)/(5) and (-1)/(3)`
Find the value of:
2.65 + 1.25
Find the value of:
1. 32 - 0.91
Find the value of:
2.12 - 0.45
Find the value of:
1.35 + 1.5
Frank solutions for Mathematics [English] Class 9 ICSE 1 Irrational Numbers Exercise 1.2
State whether the following number is rational or irrational
`(3 + sqrt(3))^2`
State whether the following number is rational or irrational
`(5 - sqrt(5))^2`
State whether the following number is rational or irrational
`(2 + sqrt(2))(2 - sqrt(2))`
State if the following is a surd. Give reasons.
`root(3)(-27)`
State whether the following number is rational or irrational
`((sqrt5)/(3sqrt(2)))^2`
Check whether the square of the following is rational or irrational:
`3sqrt(2)`
Check whether the square of the following is rational or irrational:
`3 + sqrt(2)`
Check whether the square of the following is rational or irrational:
`(3sqrt(2))/(2)`
Check whether the square of the following is rational or irrational:
`sqrt(2) + sqrt(3)`
Show that `sqrt(5)` is an irrational numbers. [Use division method]
Without using division method show that `sqrt(7)` is an irrational numbers.
Write a pair of irrational numbers whose sum is irrational.
Write a pair of irrational numbers whose sum is rational.
Write a pair of irrational numbers whose difference is irrational.
Write a pair of irrational numbers whose difference is rational.
Write a pair of irrational numbers whose product is irrational.
Write a pair of irrational numbers whose product is rational.
Compare the following:
`root(4)(12) and root(3)(15)`
Compare the following:
`root(3)(48) and sqrt(36)`
Write the following in ascending order:
`2sqrt(5), sqrt(3) and 5sqrt(2)`
Write the following in ascending order:
`2root(3)(3), 4root(3)(3) and 3root(3)(3)`
Write the following in ascending order:
`5sqrt(7), 7sqrt(5) and 6sqrt(2)`
Write the following in ascending order:
`7root(3)(5), 6root(3)(4) and 5root(3)(6)`
Write the following in descending order:
`sqrt(2), root(3)(5) and root(4)(10)`
Write the following in descending order:
`5sqrt(3), sqrt(15) and 3sqrt(5)`
Write the following in descending order:
`sqrt(6), root(3)(8) and root(4)(3)`
Insert two irrational numbers between 3 and 4.
Insert five irrational number's between `2sqrt(3) and 3sqrt(5)`.
Write two rational numbers between `sqrt(3) and sqrt(7)`
Write four rational numbers between `sqrt(2) and sqrt(3)`
State if the following is a surd. Give reasons.
`sqrt(150)`
State if the following is a surd. Give reasons.
`root(3)(4)`
State if the following is a surd. Give reasons.
`root(3)(50). root(3)(20)`
State if the following is a surd. Give reasons.
`sqrt(2 + sqrt(3)`
State if the following is a surd. Give reasons.
`root(12)(8). ÷ root(6)(6)`
Represent the number `sqrt(7)` on the number line.
Frank solutions for Mathematics [English] Class 9 ICSE 1 Irrational Numbers Exercise 1.3
Simplify by rationalising the denominator in the following.
`(3sqrt(2))/sqrt(5)`
Simplify by rationalising the denominator in the following.
`(1)/(5 + sqrt(2))`
Simplify by rationalising the denominator in the following.
`(1)/(sqrt(3) + sqrt(2))`
Simplify by rationalising the denominator in the following.
`(2)/(3 + sqrt(7)`
Simplify by rationalising the denominator in the following.
`(5)/(sqrt(7) - sqrt(2))`
Simplify by rationalising the denominator in the following.
`(42)/(2sqrt(3) + 3sqrt(2)`
Simplify by rationalising the denominator in the following.
`(sqrt(3) + 1)/(sqrt(3) - 1)`
Simplify by rationalising the denominator in the following.
`(sqrt(5) - sqrt(7))/sqrt(3)`
Simplify by rationalising the denominator in the following.
`(3 - sqrt(3))/(2 + sqrt(2)`
Simplify by rationalising the denominator in the following.
`(5 + sqrt(6))/(5 - sqrt(6)`
Simplify by rationalising the denominator in the following.
`(4 + sqrt(8))/(4 - sqrt(8)`
Simplify by rationalising the denominator in the following.
`(sqrt(15) + 3)/(sqrt(15) - 3)`
Simplify by rationalising the denominator in the following.
`(sqrt(7) - sqrt(5))/(sqrt(7) + sqrt(5)`
Simplify by rationalising the denominator in the following.
`(3sqrt(5) + sqrt(7))/(3sqrt(5) - sqrt(7)`
Simplify by rationalising the denominator in the following.
`(2sqrt(3) - sqrt(6))/(2sqrt(3) + sqrt(6)`
Simplify by rationalising the denominator in the following.
`(5sqrt(3) - sqrt(15))/(5sqrt(3) + sqrt(15)`
Simplify by rationalising the denominator in the following.
`(2sqrt(6) - sqrt(5))/(3sqrt(5) - 2sqrt(6)`
Simplify by rationalising the denominator in the following.
`(7sqrt(3) - 5sqrt(2))/(sqrt(48) + sqrt(18)`
Simplify by rationalising the denominator in the following.
`(sqrt(12) + sqrt(18))/(sqrt(75) - sqrt(50)`
Simplify the following
`(3)/(5 - sqrt(3)) + (2)/(5 + sqrt(3)`
Simplify the following
`(4 + sqrt(5))/(4 - sqrt(5)) + (4 - sqrt(5))/(4 + sqrt(5)`
Simplify the following
`(sqrt(5) - 2)/(sqrt(5) + 2) - (sqrt(5) + 2)/(sqrt(5) - 2)`
Simplify the following
`(sqrt(7) - sqrt(3))/(sqrt(7) + sqrt(3)) - (sqrt(7) + sqrt(3))/(sqrt(7) - sqrt(3)`
Simplify the following
`(sqrt(5) + sqrt(3))/(sqrt(5) - sqrt(3)) + (sqrt(5) - sqrt(3))/(sqrt(5) + sqrt(3)`
Simplify the following :
`sqrt(6)/(sqrt(2) + sqrt(3)) + (3sqrt(2))/(sqrt(6) + sqrt(3)) - (4sqrt(3))/(sqrt(6) + sqrt(2)`
Simplify the following :
`(3sqrt(2))/(sqrt(6) - sqrt(3)) - (4sqrt(3))/(sqrt(6) - sqrt(2)) + (2sqrt(3))/(sqrt(6) + 2)`
Simplify the following :
`(6)/(2sqrt(3) - sqrt(6)) + sqrt(6)/(sqrt(3) + sqrt(2)) - (4sqrt(3))/(sqrt(6) - sqrt(2)`
Simplify the following :
`(7sqrt(3))/(sqrt(10) + sqrt(3)) - (2sqrt(5))/(sqrt(6) + sqrt(5)) - (3sqrt(2))/(sqrt(15) + 3sqrt(2)`
Simplify the following :
`(4sqrt(3))/((2 - sqrt(2))) - (30)/((4sqrt(3) - 3sqrt(2))) - (3sqrt(2))/((3 + 2sqrt(3))`
If `(sqrt(2.5) - sqrt(0.75))/(sqrt(2.5) + sqrt(0.75)) = "p" + "q"sqrt(30)`, find the values of p and q.
In the following, find the values of a and b.
`(sqrt(3) - 1)/(sqrt(3) + 1) = "a" + "b"sqrt(3)`
In the following, find the values of a and b:
`(3 + sqrt(7))/(3 - sqrt(7)) = "a" + "b"sqrt(7)`
In the following, find the values of a and b:
`(5 + 2sqrt(3))/(7 + 4sqrt(3)) = "a" + "b"sqrt(3)`
In the following, find the values of a and b:
`(1)/(sqrt(5) - sqrt(3)) = "a"sqrt(5) - "b"sqrt(3)`
In the following, find the values of a and b:
`(sqrt(3) - 2)/(sqrt(3) + 2) = "a"sqrt(3) + "b"`
In the following, find the values of a and b:
`(sqrt(11) - sqrt(7))/(sqrt(11) + sqrt(7)) = "a" - "b"sqrt(77)`
In the following, find the values of a and b:
`(7sqrt(3) - 5sqrt(2))/(4sqrt(3) + 3sqrt(2)) = "a" - "b"sqrt(6)`
In the following, find the values of a and b:
`(sqrt(2) + sqrt(3))/(3sqrt(2) - 2sqrt(3)) = "a" - "b"sqrt(6)`
In the following, find the value of a and b:
`(7 + sqrt(5))/(7 - sqrt(5)) - (7 - sqrt(5))/(7 + sqrt(5)) = "a" + "b"sqrt(5)`
In the following, find the value of a and b:
`(sqrt(3) - 1)/(sqrt(3) + 1) + (sqrt(3) + 1)/(sqrt(3) - 1) = "a" + "b"sqrt(3)`
If x = `(7 + 4sqrt(3))`, find the value of
`sqrt(x) + (1)/(sqrt(x)`
If x = `(7 + 4sqrt(3))`, find the value of
`x^2 + (1)/x^2`
If x = `(7 + 4sqrt(3))`, find the values of
`x^3 + (1)/x^3`
If x = `(7 + 4sqrt(3))`, find the values of :
`(x + (1)/x)^2`
If x = `(4 - sqrt(15))`, find the values of
`(1)/x`
If x = `(4 - sqrt(15))`, find the values of
`x + (1)/x`
If x = `(4 - sqrt(15))`, find the values of
`x^2 + (1)/x^2`
If x = `(4 - sqrt(15))`, find the values of
`x^3 + (1)/x^3`
If x = `(4 - sqrt(15))`, find the values of:
`(x + (1)/x)^2`
If x = `((2 + sqrt(5)))/((2 - sqrt(5))` and y = `((2 - sqrt(5)))/((2 + sqrt(5))`, show that (x2 - y2) = `144sqrt(5)`.
If x = `((sqrt(3) + 1))/((sqrt(3) - 1)` and y = `((sqrt(3) - 1))/((sqrt(3) + 1)`, find the values of
x2 + y2
If x = `((sqrt(3) + 1))/((sqrt(3) - 1)` and y = `((sqrt(3) - 1))/((sqrt(3) + 1)`, find the values of
x3 + y3
If x = `((sqrt(3) + 1))/((sqrt(3) - 1)` and y = `((sqrt(3) - 1))/((sqrt(3) - 1)`, find the values of
x2 - y2 + xy
If x = `(1)/((3 - 2sqrt(2))` and y = `(1)/((3 + 2sqrt(2))`, find the values of
x2 + y2
If x = `(1)/((3 - 2sqrt(2))` and y = `(1)/((3 + 2sqrt(2))`, find the values of
x3 + y3
Solutions for 1: Irrational Numbers
Frank solutions for Mathematics [English] Class 9 ICSE chapter 1 - Irrational Numbers
Shaalaa.com has the CISCE Mathematics Mathematics [English] Class 9 ICSE CISCE solutions in a manner that help students grasp basic concepts better and faster. The detailed, step-by-step solutions will help you understand the concepts better and clarify any confusion. Frank solutions for Mathematics Mathematics [English] Class 9 ICSE CISCE 1 (Irrational Numbers) include all questions with answers and detailed explanations. This will clear students' doubts about questions and improve their application skills while preparing for board exams.
Further, we at Shaalaa.com provide such solutions so students can prepare for written exams. Frank textbook solutions can be a core help for self-study and provide excellent self-help guidance for students.
Concepts covered in Mathematics [English] Class 9 ICSE chapter 1 Irrational Numbers are Rational Numbers, Properties of Rational Numbers, Decimal Representation of Rational Numbers, Concept of Irrational Numbers, Concept of Real Numbers, Surds, Rationalisation of Surds, Simplifying an Expression by Rationalization of the Denominator.
Using Frank Mathematics [English] Class 9 ICSE solutions Irrational Numbers exercise by students is an easy way to prepare for the exams, as they involve solutions arranged chapter-wise and also page-wise. The questions involved in Frank Solutions are essential questions that can be asked in the final exam. Maximum CISCE Mathematics [English] Class 9 ICSE students prefer Frank Textbook Solutions to score more in exams.
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