Samacheer Kalvi solutions for Mathematics [English] Class 9 TN Board chapter 2 - Real Numbers [Latest edition]

Which arrow best shows the position of ${\displaystyle \frac{11}{3}}$ on the number line?

Find any three rational numbers between ${\displaystyle \frac{-7}{11}}$ and ${\displaystyle \frac{2}{11}}$

Find any five rational numbers between ${\displaystyle \frac{1}{4}}$ and ${\displaystyle \frac{1}{5}}$

Find any five rational numbers between 0.1 and 0.11

Find any five rational numbers between – 1 and – 2 

Express the following rational numbers into decimal and state the kind of decimal expansion

${\displaystyle \frac{2}{7}}$

Express the following rational numbers into decimal and state the kind of decimal expansion

${\displaystyle -5\frac{3}{11}}$

Express the following rational numbers into decimal and state the kind of decimal expansion

${\displaystyle \frac{22}{3}}$

Express the following rational numbers into decimal and state the kind of decimal expansion

${\displaystyle \frac{327}{200}}$

Express ${\displaystyle \frac{1}{13}}$ in decimal form. Find the length of the period of decimal

Express the rational number ${\displaystyle \frac{1}{33}}$ in recurring decimal form by using the recurring decimal expansion of ${\displaystyle \frac{1}{11}}$. Hence write ${\displaystyle \frac{71}{33}}$ in recurring decimal form.

Express the following decimal expression into rational number

${\displaystyle 0.\overline{24}}$

Express the following decimal expression into rational number

${\displaystyle 2.\overline{327}}$

Express the following decimal expression into rational number

– 5.132

Express the following decimal expression into rational number

${\displaystyle 3.1\overline{7}}$

Express the following decimal expression into rational number

${\displaystyle 17.2\overline{15}}$

Express the following decimal expression into rational number

${\displaystyle -21.213\overline{7}}$

Without actual division, find the following rational numbers have terminating decimal expansion

${\displaystyle \frac{7}{128}}$

Without actual division, find the following rational numbers have terminating decimal expansion

${\displaystyle \frac{21}{15}}$

Without actual division, find the following rational numbers have terminating decimal expansion

${\displaystyle 4\frac{9}{35}}$

Without actual division, find the following rational numbers have terminating decimal expansion

${\displaystyle \frac{219}{2200}}$

Represent the following irrational number on the number line

${\displaystyle \sqrt{3}}$

Represent the following irrational number on the number line

${\displaystyle \sqrt{4.7}}$

Represent the following irrational number on the number line

${\displaystyle \sqrt{6.5}}$

Find any two irrational numbers between 0.3010011000111…. and 0.3020020002….

Find any two irrational numbers between ${\displaystyle \frac{6}{7}}$ and ${\displaystyle \frac{12}{13}}$

Find any two irrational numbers between ${\displaystyle \sqrt{2}}$ and ${\displaystyle \sqrt{3}}$

Find any two rational numbers between 2.2360679……… and 2.236505500……….

Represent the following numbers on the number line

5.348

Represent the following numbers on the number line

${\displaystyle 6.\overline{4}}$ upto 3 decimal places

Represent the following numbers on the number line

${\displaystyle 4.\overline{73}}$ upto 4 decimal places

Write the following in the form of 5ⁿ:

625

Write the following in the form of 5ⁿ:

${\displaystyle \frac{1}{5}}$

Write the following in the form of 5ⁿ:

${\displaystyle \sqrt{5}}$

Write the following in the form of 5ⁿ:

${\displaystyle \sqrt{125}}$

Write the following in the form of 4ⁿ:

16

Write the following in the form of 4ⁿ:

8

Write the following in the form of 4ⁿ:

32

Find the value of ${\displaystyle {\left(49\right)}^{\frac{1}{2}}}$

Find the value of ${\displaystyle {\left(243\right)}^{\frac{2}{5}}}$

Find the value of ${\displaystyle 9^{\frac{-3}{2}}}$

Find the value of ${\displaystyle {\left(\frac{64}{125}\right)}^{\frac{-2}{3}}}$

Use a fractional index to write: ${\displaystyle \sqrt{5}}$

Use a fractional index to write: ${\displaystyle \sqrt[2]{7}}$

Use a fractional index to write: ${\displaystyle {\left(\sqrt[3]{49}\right)}^5}$

Use a fractional index to write: ${\displaystyle {\left(\frac{1}{\sqrt[3]{100}}\right)}^7}$

Find the 5^th root of 32

Find the 5^th root of 243

Find the 5^th root of 100000

Find the 5^th root of ${\displaystyle \frac{1024}{3125}}$

Simplify the following using addition and subtraction properties of surds:

${\displaystyle 5\sqrt{3}+18\sqrt{3}-2\sqrt{3}}$

Simplify the following using addition and subtraction properties of surds: 

${\displaystyle 4\sqrt[3]{5}+2\sqrt[3]{5}-3\sqrt[3]{5}}$

Simplify the following using addition and subtraction properties of surds: 

${\displaystyle 3\sqrt{75}+5\sqrt{48}-\sqrt{243}}$

Simplify the following using addition and subtraction properties of surds: 

${\displaystyle 5\sqrt[3]{40}+2\sqrt[3]{625}-3\sqrt[3]{320}}$

Simplify the following using multiplication and division properties of surds:

${\displaystyle \sqrt{3}\times \sqrt{5}\times \sqrt{2}}$

Simplify the following using multiplication and division properties of surds:

${\displaystyle \sqrt{35}÷\sqrt{7}}$

Simplify the following using multiplication and division properties of surds:

${\displaystyle \sqrt[3]{27}\times \sqrt[3]{8}\times \sqrt[3]{125}}$

Simplify the following using multiplication and division properties of surds:

${\displaystyle (7\sqrt{\text{a}}-5\sqrt{\text{b}})(7\sqrt{\text{a}}+5\sqrt{\text{b}})}$

Simplify the following using multiplication and division properties of surds:

${\displaystyle [\sqrt{\frac{225}{729}}-\sqrt{\frac{25}{144}}]÷\sqrt{\frac{16}{81}}}$

If ${\displaystyle \sqrt{2}}$ = 1.414, ${\displaystyle \sqrt{3}}$ = 1.732, ${\displaystyle \sqrt{5}}$ = 2.236, ${\displaystyle \sqrt{10}}$ = 3.162, then find the values of the following correct to 3 places of decimals.

${\displaystyle \sqrt{40}-\sqrt{20}}$

If ${\displaystyle \sqrt{2}}$ = 1.414, ${\displaystyle \sqrt{3}}$ = 1.732, ${\displaystyle \sqrt{5}}$ = 2.236, ${\displaystyle \sqrt{10}}$ = 3.162, then find the values of the following correct to 3 places of decimals.

${\displaystyle \sqrt{300}+\sqrt{90}-\sqrt{8}}$

Arrange surds in descending order:

${\displaystyle \sqrt[3]{5},\sqrt[9]{4},\sqrt[6]{3}}$

Arrange surds in descending order:

${\displaystyle \sqrt[2]{\sqrt[3]{5}},\sqrt[3]{\sqrt[4]{7}},\sqrt{\sqrt{3}}}$

Can you get a pure surd when you find the sum of two surds Justify answer with an example

Can you get a pure surd when you find the difference of two surds Justify answer with an example

Can you get a pure surd when you find the product of two surds Justify answer with an example.

Can you get a pure surd when you find the quotient of two surds Justify answer with an example

Can you get a rational number when you compute the sum of two surds Justify answer with an example

Can you get a rational number when you compute the difference of two surds Justify answer with an example

Can you get a rational number when you compute the product of two surds Justify answer with an example

Can you get a rational number when you compute the quotient of two surds Justify answer with an example

Rationalise the denominator ${\displaystyle \frac{1}{\sqrt{50}}}$

Rationalise the denominator ${\displaystyle \frac{5}{3\sqrt{5}}}$

Rationalise the denominator ${\displaystyle \frac{\sqrt{75}}{\sqrt{18}}}$

Rationalise the denominator ${\displaystyle \frac{3\sqrt{5}}{\sqrt{6}}}$

Rationalise the denominator and simplify ${\displaystyle \frac{\sqrt{48}+\sqrt{32}}{\sqrt{27}-\sqrt{18}}}$

Rationalise the denominator and simplify ${\displaystyle \frac{5\sqrt{3}+\sqrt{2}}{\sqrt{3}+\sqrt{2}}}$

Rationalise the denominator and simplify ${\displaystyle \frac{2\sqrt{6}-\sqrt{5}}{3\sqrt{5}-2\sqrt{6}}}$

Rationalise the denominator and simplify ${\displaystyle \frac{\sqrt{5}}{\sqrt{6}+2}-\frac{\sqrt{5}}{\sqrt{6}-2}}$

Find the value of a and b if ${\displaystyle \frac{\sqrt{7}-2}{\sqrt{7}+2}=\text{a}\sqrt{7}+\text{b}}$

If x = ${\displaystyle \sqrt{5}+2}$, then find the value of ${\displaystyle x^2+\frac{1}{x^2}}$

Given ${\displaystyle \sqrt{2}}$ = 1.414, find the value of ${\displaystyle \frac{8-5\sqrt{2}}{3-2\sqrt{2}}}$ (to 3 places of decimals).

Represent the following numbers in the scientific notation:

569430000000

Represent the following numbers in the scientific notation:

2000.57

Represent the following numbers in the scientific notation:

0.0000006000

Represent the following number in the scientific notation:

0.0009000002

Write the following numbers in decimal form:

3.459 × 10⁶  

Write the following numbers in decimal form:

5.678 × 10⁴ 

Write the following numbers in decimal form:

1.00005 × 10⁻⁵ 

Write the following numbers in decimal form:

2.530009 × 10⁻⁷ 

Represent the following numbers in scientific notation:

(300000)² × (20000)⁴ 

Represent the following numbers in scientific notation:

(0.000001)¹¹ ÷ (0.005)³ 

Represent the following numbers in scientific notation:

${\displaystyle \{{\left(0.00003\right)}^6\times {\left(0.00005\right)}^4\}÷\{{\left(0.009\right)}^3\times {\left(0.05\right)}^2\}}$

Represent the following information in scientific notation:

The world population is nearly 7000,000,000

Represent the following information in scientific notation:

One light year means the distance 9460528400000000 km

Represent the following information in scientific notation:

Mass of an electron is 0.000 000 000 000 000 000 000 000 000 00091093822 kg

Simplify: (2.75 × 10⁷) + (1.23 × 10⁸)

Simplify: (1.598 × 10¹⁷) – (4.58 × 10¹⁵)

Simplify: (1.02 × 10¹⁰) × (1.20 × 10⁻³)

Simplify: (8.41 × 10⁴) ÷ (4.3 × 10⁵)

If n is a natural number then ${\displaystyle \sqrt{\text{n}}}$ is

Which of the following is not true?

Which one of the following, regarding sum of two irrational numbers, is true?

Which one of the following has a terminating decimal expansion?

Which one of the following is an irrational number

An irrational number between 2 and 2.5 is

The smallest rational number by which ${\displaystyle \frac{1}{3}}$ should be multiplied so that its decimal expansion terminates with one place of decimal is

If ${\displaystyle \frac{1}{7}=0.\overline{142857}}$ then the value of ${\displaystyle \frac{5}{7}}$ is

Find the odd one out of the following.

${\displaystyle 0.\overline{34}+ 0.3\overline{4}}$ =

Which of the following statement is false?

Which one of the following is not a rational number?

${\displaystyle \sqrt{27}+\sqrt{12}}$ =

If ${\displaystyle \sqrt{80}=\text{k}\sqrt{5}}$, then k = 

${\displaystyle 4\sqrt{7}\times 2\sqrt{3}}$ =

When written with a rational denominator, the expression ${\displaystyle \frac{2\sqrt{3}}{3\sqrt{2}}}$ can be simplified as 

When ${\displaystyle {(2\sqrt{5}-\sqrt{2})}^2}$ is simplified, we get

${\displaystyle {\left(0.000729\right)}^{\frac{-3}{4}}\times {\left(0.09\right)}^{\frac{-3}{4}}}$ = ______

If ${\displaystyle \sqrt{9^x}=\sqrt[3]{9^2}}$, then x = ______

The length and breadth of a rectangular plot are 5 × 10⁵ and 4 × 10⁴ metres respectively. Its area is ______