Question

simplify the following expression:
(I) (5+√7) (2+√5)
(ii)(√3+√7)²
(iii) (5+√5) (5-√5)
(iv) (√11 – √7) (√11+ √7)​

Answer 1

Answer:

1.

$10 + 5 \sqrt{5 } + 2 \sqrt{7} + 35 \\ \\ = 45 + 7 \sqrt{12}$

2.

$( \sqrt{3} ) { }^{2} + ( \sqrt{7} ) ^{2} + 2 \times \sqrt{3} \times \sqrt{7 } \\ \\ = 3 + 7 + 2 \sqrt{21 } \\ \\ = 10 + 2 \sqrt{21}$

3.

$(5) {}^{2} - ( \sqrt{5} ) {}^{2} \\ 25 - 5 \\ = 20$

4.

$( \sqrt{11} ) {}^{2} - ( \sqrt{7} ) {}^{2} \\ 11 - 7 \\ = 6$

Step-by-step explanation:

1. In this we have to use cross multiplication method.

2. we have to use identity (a+b)^2=a^2+b^2+2×a×b

3

.we have to use identity a^2-b^2

4.we have to use identity a^2-b^2