Solve frac{5*sqrt{3}}{sqrt{21}}

$$\frac{ 5 \times \sqrt{ 3 } }{ \sqrt{ 21 } }$$

Evaluate

$$\frac{5\sqrt{7}}{7}\approx 1.889822365$$

Solution Steps

Rationalize the denominator of \frac{5\sqrt{3}}{\sqrt{21}} by multiplying numerator and denominator by \sqrt{21}.

$$\frac{5\sqrt{3}\sqrt{21}}{\left(\sqrt{21}\right)^{2}}$$

The square of \sqrt{21} is 21.

$$\frac{5\sqrt{3}\sqrt{21}}{21}$$

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}.

$$\frac{5\sqrt{3}\sqrt{3}\sqrt{7}}{21}$$

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

$$\frac{5\times 3\sqrt{7}}{21}$$

Multiply 5 and 3 to get 15.

$$\frac{15\sqrt{7}}{21}$$

Divide 15\sqrt{7} by 21 to get \frac{5}{7}\sqrt{7}.

$$\frac{5}{7}\sqrt{7}$$