Solve sqrt{1471.2/0.37}

$$\sqrt{ \frac{ 1471.2 }{ 0.37 } }$$

Evaluate

$$\frac{4\sqrt{340215}}{37}\approx 63.057245549$$

Solution Steps

Expand \frac{1471.2}{0.37} by multiplying both numerator and the denominator by 100.

$$\sqrt{\frac{147120}{37}}$$

Rewrite the square root of the division \sqrt{\frac{147120}{37}} as the division of square roots \frac{\sqrt{147120}}{\sqrt{37}}.

$$\frac{\sqrt{147120}}{\sqrt{37}}$$

Factor 147120=4^{2}\times 9195. Rewrite the square root of the product \sqrt{4^{2}\times 9195} as the product of square roots \sqrt{4^{2}}\sqrt{9195}. Take the square root of 4^{2}.

$$\frac{4\sqrt{9195}}{\sqrt{37}}$$

Rationalize the denominator of \frac{4\sqrt{9195}}{\sqrt{37}} by multiplying numerator and denominator by \sqrt{37}.

$$\frac{4\sqrt{9195}\sqrt{37}}{\left(\sqrt{37}\right)^{2}}$$

The square of \sqrt{37} is 37.

$$\frac{4\sqrt{9195}\sqrt{37}}{37}$$

To multiply \sqrt{9195} and \sqrt{37}, multiply the numbers under the square root.

$$\frac{4\sqrt{340215}}{37}$$