Question

find a and b if 3+√24+√75=a+b√3

Answer 1

Answer:

$3 + \sqrt{24} + \sqrt{75} = a + b \sqrt{3} \\ 3 + \sqrt{6 \times 4} + \sqrt{25 \times 3} = a + b \sqrt{3} \\ 3 + 2 \sqrt{6} + 5 \sqrt{3} = a + b \sqrt{3} \\3 + 2 \sqrt{2} \times \sqrt{3} + 5 \sqrt{3} = a + b \sqrt{3} \\ 3 + \sqrt{3} ( 2\sqrt{2} + 5) = a + b \sqrt{3} \\ equating \: like \: terms \: on \: both \: \\ sides \: \: we \: find \: \\ a = 3 \\ b = 2\sqrt{2} + 5 \:$