CBSE Question Paper for Class 10 Maths
2018 Question 7

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.

Video Explanation

Explanatory Answer

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.