# CBSE Class 10 Maths Sample Question Paper 2019 | Q7

#### Internal Choice 2 | 2 Mark Question | Real Numbers - Irrational Numbers

This 2019 CBSE class 10 Maths sample paper 2 mark question is from real numbers. How to prove whether a given number is an irrational number? A standard NCERT text book question.

Question 7B: Show that 7 − √5 is irrational, given that √5 is irrational.

## NCERT Solution to Class 10 Maths

### Explanatory Answer - Alternative 2

Let us assume the contrary that 7 - √5 is rational.

So, we can express 7 - √5 = $\frac{a}{b}$ where a and b are co-prime integers and b ≠ 0.
So, √5 = 7 - $\frac{a}{b}$ = $\frac{7b - a}{b}$

Because a, b, and 7 are integers $\frac{7b - a}{b}$ is rational, implying that √5 is rational.
But this contradicts with the fact that √5 is irrational.
The contradiction is because of the incorrect assumption that 7 - √5 is rational.
∴ We can conclude that 7 - √5 is irrational.

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