Number System | Number System - Exercise 1.5

Question

$\frac{1}{\sqrt{2}}$ is a rational number.

Accepted Answer

Multiplying and dividing numerator and denominator by √2 we get,

$\frac{1}{\sqrt{2}}\times\frac{\sqrt{2}}{\sqrt{2}}=\frac{\sqrt{2}}{2}(∵\sqrt{2}\times\sqrt{2}=2)$

We know that, √2 = 1.4142…

Then, $\frac{\sqrt{2}}{2}=\frac{1.4142}{2}=0.7071..$

Since the number , 0.7071..is non-terminating non-recurring, $\frac{1}{\sqrt{2}}$ is an irrational number.

Question 6