Question

√5+√3 divided by 2√5-3√3 = a+b√15

Answer 1

$\sqrt{5} + \sqrt{3 } \div 2 \sqrt{5} - 3 \sqrt{3} \times 2 \sqrt{5} + 3 \sqrt{3 } 2 \sqrt{5} + 3 \sqrt{3} \\ = 10 + 3 \sqrt{15} + 2 \sqrt{15} + 9 \div 20 - 18 \\ = 19 + 5 \sqrt{15} \div 2 \\ so \: a = 19 \div 2 \: and \: b = 5 \div 2$

Answer 2

√5 × √15 = √75 (= 15× 5)

= √25 × √3

= 5 √3

 

(1 + √3)(2 - √8) [The brackets are expanded as usual]

= 2 - √8 + 2√3 - √24

= 2 - 2√2 + 2√3 - 2√6