Solve 30sqrt{858/151}

$$30 \sqrt{ \frac{ 858 }{ 151 } }$$

Evaluate

$$\frac{30\sqrt{129558}}{151}\approx 71.511588465$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{858}{151}} as the division of square roots \frac{\sqrt{858}}{\sqrt{151}}.

$$30\times \frac{\sqrt{858}}{\sqrt{151}}$$

Rationalize the denominator of \frac{\sqrt{858}}{\sqrt{151}} by multiplying numerator and denominator by \sqrt{151}.

$$30\times \frac{\sqrt{858}\sqrt{151}}{\left(\sqrt{151}\right)^{2}}$$

The square of \sqrt{151} is 151.

$$30\times \frac{\sqrt{858}\sqrt{151}}{151}$$

To multiply \sqrt{858} and \sqrt{151}, multiply the numbers under the square root.

$$30\times \frac{\sqrt{129558}}{151}$$

Express 30\times \frac{\sqrt{129558}}{151} as a single fraction.

$$\frac{30\sqrt{129558}}{151}$$