Solve 7*sqrt{458/258}

$$7 \times \sqrt{ \frac{ 458 }{ 258 } }$$

Evaluate

$$\frac{7\sqrt{29541}}{129}\approx 9.326547921$$

Solution Steps

Reduce the fraction \frac{458}{258} to lowest terms by extracting and canceling out 2.

$$7\sqrt{\frac{229}{129}}$$

Rewrite the square root of the division \sqrt{\frac{229}{129}} as the division of square roots \frac{\sqrt{229}}{\sqrt{129}}.

$$7\times \frac{\sqrt{229}}{\sqrt{129}}$$

Rationalize the denominator of \frac{\sqrt{229}}{\sqrt{129}} by multiplying numerator and denominator by \sqrt{129}.

$$7\times \frac{\sqrt{229}\sqrt{129}}{\left(\sqrt{129}\right)^{2}}$$

The square of \sqrt{129} is 129.

$$7\times \frac{\sqrt{229}\sqrt{129}}{129}$$

To multiply \sqrt{229} and \sqrt{129}, multiply the numbers under the square root.

$$7\times \frac{\sqrt{29541}}{129}$$

Express 7\times \frac{\sqrt{29541}}{129} as a single fraction.

$$\frac{7\sqrt{29541}}{129}$$