Solve frac{sqrt{12}sqrt{20}}{sqrt{15}}

$$\frac { \sqrt { 12 } \sqrt { 20 } } { \sqrt { 15 } }$$

Evaluate

$$4$$

Solution Steps

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

$$\frac{2\sqrt{3}\sqrt{20}}{\sqrt{15}}$$

Factor 20=2^{2}\times 5. Rewrite the square root of the product \sqrt{2^{2}\times 5} as the product of square roots \sqrt{2^{2}}\sqrt{5}. Take the square root of 2^{2}.

$$\frac{2\sqrt{3}\times 2\sqrt{5}}{\sqrt{15}}$$

Multiply 2 and 2 to get 4.

$$\frac{4\sqrt{3}\sqrt{5}}{\sqrt{15}}$$

To multiply \sqrt{3} and \sqrt{5}, multiply the numbers under the square root.

$$\frac{4\sqrt{15}}{\sqrt{15}}$$

Rationalize the denominator of \frac{4\sqrt{15}}{\sqrt{15}} by multiplying numerator and denominator by \sqrt{15}.

$$\frac{4\sqrt{15}\sqrt{15}}{\left(\sqrt{15}\right)^{2}}$$

The square of \sqrt{15} is 15.

$$\frac{4\sqrt{15}\sqrt{15}}{15}$$

Multiply \sqrt{15} and \sqrt{15} to get 15.

$$\frac{4\times 15}{15}$$

Multiply 4 and 15 to get 60.

$$\frac{60}{15}$$

Divide 60 by 15 to get 4.

$$4$$

Factor

$$2^{2}$$