Question

prove that root 2 + root 5 is an irrational number

Answer 1

refer to the attachment ......

Answer 2

HOLA USER ✌

HERE'S YOUR ANSWER FRIEND,

◾ Let √2 + √5 be a rational number.

==> √2 + √5 = a/b

On Squaring both the sides we have,

==> (√2 + √5)² = (a/b)²

==> √2² + 2(√2)(√5) + √5² = (a/b)²............{using the identity (a + b)² = a² + 2ab + b²}

==> 2 + 2√10 + 5 = a²/b²

==> 2√10 + 7 = a²/b²

==> 2√10 = a²/b² - 7

==> 2√10 = (a² - 7b²)/b²

==> √10 = (a² - 7b²)/2b²

==> Here,

(a² - 7b²)/2b² is a rational number.

But, √10 is an irrational number.

Therefore,

Our assumption is proved wrong.

Hence,

√10 is an irrational number.

==> √2 + √5 is also an irrational number.

HOPE IT HELPS YOU.

(^_^)