Question

Proove root 3 and root 3 + 5 is an irrational no

Answer 1

Step-by-step explanation:

$let \: \sqrt{3} = \frac{a}{b}$

where a and b both are integer and b is not equal to 1 .

$( \frac{a}{b})^{2} = \: 3$

${a}^{2} = 3 \cdot {b}^{2}$

For Perfect square a number should have odd number of divisors .

Here b is having odd number of divisor but a not having odd number of divisor according to the conclusion we got through calculation .

But we had taken a as a integer here our statement contradicts and the number is irrational .

Same by adding one integer the number still remains irrational.