Solve sqrt{48*9225030/314*80}

$$\sqrt{ \frac{ 48 \times 9225030 }{ 314 \times 80 } }$$

Evaluate

$$\frac{213\sqrt{9577}}{157}\approx 132.768391795$$

Solution Steps

Cancel out 2\times 8\times 10 in both numerator and denominator.

$$\sqrt{\frac{3\times 922503}{157}}$$

Multiply 3 and 922503 to get 2767509.

$$\sqrt{\frac{2767509}{157}}$$

Rewrite the square root of the division \sqrt{\frac{2767509}{157}} as the division of square roots \frac{\sqrt{2767509}}{\sqrt{157}}.

$$\frac{\sqrt{2767509}}{\sqrt{157}}$$

Factor 2767509=213^{2}\times 61. Rewrite the square root of the product \sqrt{213^{2}\times 61} as the product of square roots \sqrt{213^{2}}\sqrt{61}. Take the square root of 213^{2}.

$$\frac{213\sqrt{61}}{\sqrt{157}}$$

Rationalize the denominator of \frac{213\sqrt{61}}{\sqrt{157}} by multiplying numerator and denominator by \sqrt{157}.

$$\frac{213\sqrt{61}\sqrt{157}}{\left(\sqrt{157}\right)^{2}}$$

The square of \sqrt{157} is 157.

$$\frac{213\sqrt{61}\sqrt{157}}{157}$$

To multiply \sqrt{61} and \sqrt{157}, multiply the numbers under the square root.

$$\frac{213\sqrt{9577}}{157}$$