Simplify the following radicals. 1 (30)/(sqrt (20))cdot square =square =square

To simplify the given expression, we need to rationalize the denominator and simplify the fraction.<br /><br />Given expression: $\frac{30}{\sqrt{20}}$<br /><br />Step 1: Rationalize the denominator by multiplying both the numerator and denominator by $\sqrt{20}$.<br />$\frac{30}{\sqrt{20}} \cdot \frac{\sqrt{20}}{\sqrt{20}} = \frac{30\sqrt{20}}{20}$<br /><br />Step 2: Simplify the fraction by dividing both the numerator and denominator by their greatest common divisor (GCD), which is 10.<br />$\frac{30\sqrt{20}}{20} = \frac{3\sqrt{20}}{2}$<br /><br />Step 3: Simplify the radical in the numerator.<br />$\frac{3\sqrt{20}}{2} = \frac{3\sqrt{4 \cdot 5}}{2} = \frac{3 \cdot 2\sqrt{5}}{2} = 3\sqrt{5}$<br /><br />Therefore, the simplified form of the given expression is $3\sqrt{5}$.