Questions: Rationalize the denominator and simplify, if possible. sqrt(60)/sqrt(5)

Solution Steps

First, simplify the expression by dividing the square roots:

\[ \frac{\sqrt{60}}{\sqrt{5}} = \sqrt{\frac{60}{5}} \]

Calculate the fraction inside the square root:

\[ \frac{60}{5} = 12 \]

Thus, the expression becomes:

\[ \sqrt{12} \]

Simplify \(\sqrt{12}\) by expressing 12 as a product of its prime factors:

\[ 12 = 4 \times 3 = 2^2 \times 3 \]

Therefore,

\[ \sqrt{12} = \sqrt{2^2 \times 3} = \sqrt{2^2} \times \sqrt{3} = 2\sqrt{3} \]

Final Answer