Question

(root2+1)^2 is a irrationa number ? justify your answer

Answer 1

heya...

Here is your answer...

$( \sqrt{2} + 1)^{2}$
$(a + b)^{2} = {a}^{2} + {b}^{2} + 2(a)(b)$
${ \sqrt{2} }^{2} + {1}^{2} + 2( \sqrt{2} )(1)$
$2 + 1 + 2 \sqrt{2}$
$3 + 2 \sqrt{2}$
Therefore
$( \sqrt{2} + 1)^{2}$
is a irrational number.

It may help you...☺☺

Answer 2

Here is your answer
$( \sqrt{2} + 1) {}^{2} \\ = ( \sqrt{2} ) {}^{2} + 1 + 2 \times \sqrt{2 } \\ = 2 + 1 + 2 \sqrt{2} \\ = 3 + 2 \sqrt{2}$
On Solving it we get it which is an irrational number
Hope it helps you