Question

Simplify the following expression \sqrt(75)+\sqrt(108)=a\sqrt(b) If the expression is simplified completely, what does a equal and what does b equal

Answer 1

$\sqrt{75} + \sqrt{108} = a \sqrt{b}$

$\sqrt{75} = \sqrt{3 \times 5 {}^{2} } = 5 \sqrt{3}$

$\sqrt{108} = \sqrt{2 {}^{2} + 3 {}^{3} } = 2 \times 3 \sqrt{3} = 6 \sqrt{3}$

$\sqrt{75} + \sqrt{108} = 5\sqrt{3} + 6 \sqrt{3} = 11 \sqrt{3}$

$a = 11$

$b = 3$