Solve 332sqrt{37/273}

$$332 \sqrt{ \frac{ 37 }{ 273 } }$$

Evaluate

$$\frac{332\sqrt{10101}}{273}\approx 122.224317886$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{37}{273}} as the division of square roots \frac{\sqrt{37}}{\sqrt{273}}.

$$332\times \frac{\sqrt{37}}{\sqrt{273}}$$

Rationalize the denominator of \frac{\sqrt{37}}{\sqrt{273}} by multiplying numerator and denominator by \sqrt{273}.

$$332\times \frac{\sqrt{37}\sqrt{273}}{\left(\sqrt{273}\right)^{2}}$$

The square of \sqrt{273} is 273.

$$332\times \frac{\sqrt{37}\sqrt{273}}{273}$$

To multiply \sqrt{37} and \sqrt{273}, multiply the numbers under the square root.

$$332\times \frac{\sqrt{10101}}{273}$$

Express 332\times \frac{\sqrt{10101}}{273} as a single fraction.

$$\frac{332\sqrt{10101}}{273}$$