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NCERT Solutions Class 9 Mathematics Solutions for Number System - Exercise 1.5 in Chapter 1 - Number System

Question 6 Number System - Exercise 1.5

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

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.

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