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Number System | Number System - Exercise 1.5

Question 6

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

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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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Question 6

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

Looking to do well in your science exam ? Learn from an expert tutor. Book a free class!

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.

Our top 5% students will be awarded a special scholarship to Lido.

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