# CBSE Question Paper for Class 10 Maths2018 Question 7

###### CBSE Solved Question Paper 2 Mark | Real Numbers

This 2018 CBSE class 10 Maths 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 7: Given that √2 is irrational, prove that (5 + 3√2) is an irrational number.

## NCERT Solution to Class 10 Maths

#### With Videos

Let us assume the contrary.

i.e; 5 + 3√2 is rational

∴ 5 + 3√2 = $$frac{a}{b}$, where ‘a’ and ‘b’ are coprime integers and b ≠ 0 3√2 = $\frac{a}{b}$ – 5 3√2 = $\frac{a - 5b}{b}$ Or √2 = $\frac{a - 5b}{3b}$ Because ‘a’ and ‘b’ are integers $\frac{a - 5b}{3b}$ is rational That contradicts the fact that √2 is irrational. The contradiction is because of the incorrect assumption that$5 + 3√2) is rational.

So, 5 + 3√2 is irrational.

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