Advertisements
Advertisements
Question
Prove that of the numbers `3 sqrt(7)` is irrational:
Solution
Let `3 sqrt(7)` be rational.
`1/3 ×3 sqrt(7)= sqrt(7)` = rational [∵Product of two rational is rational]
This contradicts the fact that `sqrt(7)` is irrational.
The contradiction arises by assuming `3 sqrt(7)` is rational.
Hence, `3 sqrt(7)` is irrational.
APPEARS IN
RELATED QUESTIONS
Examine, whether the following number are rational or irrational:
`(sqrt2+sqrt3)^2`
Find two irrational numbers between 0.5 and 0.55.
State whether the following statement is true or false. Justify your answer.
Every point on the number line is of the form `sqrt m`, where m is a natural number.
State, whether the following numbers is rational or not : ( 2 + √2 )2
State, whether the following numbers is rational or not : ( 3 - √3 )2
Prove that the following number is irrational: √3 + √2
Write a pair of irrational numbers whose sum is irrational.
Insert two irrational numbers between 3 and 4.
`sqrt(12)/sqrt(3)` is not a rational number as `sqrt(12)` and `sqrt(3)` are not integers.
Find whether the variable z represents a rational or an irrational number:
z2 = 0.04
