Question

find the product
$5 \sqrt{2}(3 + \sqrt{2})(5 + \sqrt{2})$

Answer 1

5√2[(3+√2)(5+√2)]

= 5√2[3(5+√2)+√2(5+√2)]

= 5√2[15+3√2+5√2+√4]

= 5√2[15+8√2+2]

= 5√2[17+8√2]

= 17(5√2)+8√2(5√2)

= 85√2+40√4

= 85√2+40×2

= 85√2+80