# How do you simplify sqrt(33a^11b^11) times sqrt(3)?

Jul 31, 2016

$3 {a}^{5} {b}^{5} \sqrt{11 a b}$

#### Explanation:

The two roots can be combined into a single root because they are being multiplied. Write the numbers as the product of the prime factors.

$\sqrt{3 \times 3 \times 11 {a}^{11} {b}^{11}}$

Factors with even powers are squares and have a square root.

=$\sqrt{{3}^{2} \times 11 \times {a}^{10} {b}^{10} a b}$

=$3 {a}^{5} {b}^{5} \sqrt{11 a b}$