Solve sqrt{4.8*9225030/3.14*80}

$$\sqrt{ \frac{ 4.8 \times 9225030 }{ 3.14 \times 80 } }$$

Evaluate

$$\frac{213\sqrt{95770}}{157}\approx 419.85051935$$

Solution Steps

Cancel out 10 in both numerator and denominator.

$$\sqrt{\frac{4.8\times 922503}{3.14\times 8}}$$

Multiply 4.8 and 922503 to get 4428014.4.

$$\sqrt{\frac{4428014.4}{3.14\times 8}}$$

Multiply 3.14 and 8 to get 25.12.

$$\sqrt{\frac{4428014.4}{25.12}}$$

Expand \frac{4428014.4}{25.12} by multiplying both numerator and the denominator by 100.

$$\sqrt{\frac{442801440}{2512}}$$

Reduce the fraction \frac{442801440}{2512} to lowest terms by extracting and canceling out 16.

$$\sqrt{\frac{27675090}{157}}$$

Rewrite the square root of the division \sqrt{\frac{27675090}{157}} as the division of square roots \frac{\sqrt{27675090}}{\sqrt{157}}.

$$\frac{\sqrt{27675090}}{\sqrt{157}}$$

Factor 27675090=213^{2}\times 610. Rewrite the square root of the product \sqrt{213^{2}\times 610} as the product of square roots \sqrt{213^{2}}\sqrt{610}. Take the square root of 213^{2}.

$$\frac{213\sqrt{610}}{\sqrt{157}}$$

Rationalize the denominator of \frac{213\sqrt{610}}{\sqrt{157}} by multiplying numerator and denominator by \sqrt{157}.

$$\frac{213\sqrt{610}\sqrt{157}}{\left(\sqrt{157}\right)^{2}}$$

The square of \sqrt{157} is 157.

$$\frac{213\sqrt{610}\sqrt{157}}{157}$$

To multiply \sqrt{610} and \sqrt{157}, multiply the numbers under the square root.

$$\frac{213\sqrt{95770}}{157}$$