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

`√(75) + √(108) = a √(b)`

`√(75) = \sqrt{3 * 5 {}^(2) } = 5 √(3)`

`√(108) = \sqrt{2 {}^(2) + 3 {}^(3) } = 2 * 3 √(3) = 6 √(3)`

`√(75) + √(108) = 5√(3) + 6 √(3) = 11 √(3)`

`a = 11`

`b = 3`