Question

show that -3+2√5 is an irrational number. ​

Answer 1

Question:-

show that -3+2√5 is an irrational number. ​

Answer:-

Let us assume that (-3+2√5 ) is a rational.

Subtract given number form -3, considering -3 is a rational number.

As we know, Difference of two rational numbers is a rational.

-3 – (-3 + 2√5 ) is rational

2√5 is rational

Which is only possible if 2 is rational and √5 is rational

As we know, product of two rational number is rational.

But the fact is √5 is an irrational.

Which is contradict to our assumption.

Hence, 4 – 5√2 is irrational. Hence Proved