Solve 4sqrt{21}divsqrt{3}

$$4 \sqrt { 21 } \div \sqrt { 3 }$$

Evaluate

$$4\sqrt{7}\approx 10.583005244$$

Solution Steps

Rationalize the denominator of \frac{4\sqrt{21}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{4\sqrt{21}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{4\sqrt{21}\sqrt{3}}{3}$$

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

$$\frac{4\sqrt{3}\sqrt{7}\sqrt{3}}{3}$$

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

$$\frac{4\times 3\sqrt{7}}{3}$$

Cancel out 3 and 3.

$$4\sqrt{7}$$