Question

evaluate(root2+root 3)^2 - (root 5- root2)^2​

Answer 1

Step-by-step explanation:

(√2+√3)²-(√5-√2)²

=2+2.√2.√3+3-(5-2.√5.√2+2)

=5+2√6-(7-2√10)

=-2+2√6+2√10

=2(-1+√6+√10)

Answer 2

Answer:

$2( \sqrt{6} + \sqrt{10} - 1)$

Step-by-step explanation:

$( \sqrt{2} + \sqrt{3} ) {}^{2} - ( \sqrt{5} - \sqrt{2} ) {}^{2} \\ \\ = ( \sqrt{2} ) {}^{2} + ( \sqrt{3} ) {}^{2} + 2 \times \sqrt{2} \times \sqrt{3} \\ \: \: \: - ( ( \sqrt{5} ) {}^{2} + ( \sqrt{2} ) {}^{2} - 2 \times \sqrt{5} \times \sqrt{2} \\ \\ = 2 + 3 + 2 \sqrt{6} - (5 + 2 - 2 \sqrt{10} ) \\ \\ = 5 + 2 \sqrt{6} - (7 - 2 \sqrt{10} ) \\ \\ = 5 + 2 \sqrt{6} - 7 + 2 \sqrt{10} \\ \\ = - 2 + 2 \sqrt{6} + 2 \sqrt{10} \\ \\ = 2 \sqrt{6} + 2 \sqrt{10} - 2 \\ \\ = 2( \sqrt{6} + \sqrt{10} - 1)$

We are using simple rules of evaluation in mathematics to arrive at our answer.