Solve frac{sqrt{21}*sqrt{7}}{sqrt{3}}

$$\frac { \sqrt { 21 } \times \sqrt { 7 } } { \sqrt { 3 } }$$

Evaluate

$$7$$

Solution Steps

Factor 21=7\times 3. Rewrite the square root of the product \sqrt{7\times 3} as the product of square roots \sqrt{7}\sqrt{3}.

$$\frac{\sqrt{7}\sqrt{3}\sqrt{7}}{\sqrt{3}}$$

Multiply \sqrt{7} and \sqrt{7} to get 7.

$$\frac{7\sqrt{3}}{\sqrt{3}}$$

Rationalize the denominator of \frac{7\sqrt{3}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{7\sqrt{3}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{7\sqrt{3}\sqrt{3}}{3}$$

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$\frac{7\times 3}{3}$$

Multiply 7 and 3 to get 21.

$$\frac{21}{3}$$

Divide 21 by 3 to get 7.

$$7$$

Factor

$$7$$