Solve 4sqrt{21/20}

$$4 \sqrt{ \frac{ 21 }{ 20 } }$$

Evaluate

$$\frac{2\sqrt{105}}{5}\approx 4.098780306$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{21}{20}} as the division of square roots \frac{\sqrt{21}}{\sqrt{20}}.

$$4\times \frac{\sqrt{21}}{\sqrt{20}}$$

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}.

$$4\times \frac{\sqrt{21}}{2\sqrt{5}}$$

Rationalize the denominator of \frac{\sqrt{21}}{2\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$4\times \frac{\sqrt{21}\sqrt{5}}{2\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$4\times \frac{\sqrt{21}\sqrt{5}}{2\times 5}$$

To multiply \sqrt{21} and \sqrt{5}, multiply the numbers under the square root.

$$4\times \frac{\sqrt{105}}{2\times 5}$$

Multiply 2 and 5 to get 10.

$$4\times \frac{\sqrt{105}}{10}$$

Express 4\times \frac{\sqrt{105}}{10} as a single fraction.

$$\frac{4\sqrt{105}}{10}$$

Divide 4\sqrt{105} by 10 to get \frac{2}{5}\sqrt{105}.

$$\frac{2}{5}\sqrt{105}$$