Question

simplify the following expresstions.
i) (5+√7) (2+√5) ii. (5+√5) (5-√5)
iii. (√3+√7)² iv. √11-√7) (√11+√7)​

Answer 1

Answer:

$(i)10 + 5 \sqrt{5} + \sqrt{7} 2 + \sqrt{35 } \\ (ii)5 {}^{2} - ( \sqrt{5} ) {}^{2} \\ = 25 - 5 = 20 \\ (iii)( \sqrt{3} + \sqrt{7} ) {}^{2} \\ = \sqrt{3} \ ^2 + 2 \sqrt{21} + 7 \\ (iv) ( \sqrt{} {11} - 7)( \sqrt{11} + 7) \\ = 11 - 49 \\ = - 38$

(iv)

$( \sqrt{11} - \sqrt{7} )( \sqrt{11} + \sqrt{7} ) \\ = 11 - 7 \\ = 4$