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.

Related Questions

**Simplify** **(√5+√2)<sup>2</sup>**

Exercises

Number System - Exercise 1.1

Number System - Exercise 1.2

Number System - Exercise 1.3

Number System - Exercise 1.4

Number System - Exercise 1.5

Number System - Exercise 1.6

Chapters

Number System

Polynomials

Coordinate Geometry

Linear Equations in Two Variables

Introduction to Euclids Geometry

Lines and Angles

Triangles

Quadrilaterals

Areas of Parallelograms and Triangles

Circles

Constructions

Heron’s Formula

Surface Areas and Volumes

Statistics

Probability