Solve 562*2950*sqrt{10div3600}

$$562 \times 2950 \times \sqrt{ 10 \div 3600 }$$

Evaluate

$$\frac{82895\sqrt{10}}{3}\approx 87379.002213219$$

Solution Steps

Multiply 562 and 2950 to get 1657900.

$$1657900\sqrt{\frac{10}{3600}}$$

Reduce the fraction \frac{10}{3600} to lowest terms by extracting and canceling out 10.

$$1657900\sqrt{\frac{1}{360}}$$

Rewrite the square root of the division \sqrt{\frac{1}{360}} as the division of square roots \frac{\sqrt{1}}{\sqrt{360}}.

$$1657900\times \frac{\sqrt{1}}{\sqrt{360}}$$

Calculate the square root of 1 and get 1.

$$1657900\times \frac{1}{\sqrt{360}}$$

Factor 360=6^{2}\times 10. Rewrite the square root of the product \sqrt{6^{2}\times 10} as the product of square roots \sqrt{6^{2}}\sqrt{10}. Take the square root of 6^{2}.

$$1657900\times \frac{1}{6\sqrt{10}}$$

Rationalize the denominator of \frac{1}{6\sqrt{10}} by multiplying numerator and denominator by \sqrt{10}.

$$1657900\times \frac{\sqrt{10}}{6\left(\sqrt{10}\right)^{2}}$$

The square of \sqrt{10} is 10.

$$1657900\times \frac{\sqrt{10}}{6\times 10}$$

Multiply 6 and 10 to get 60.

$$1657900\times \frac{\sqrt{10}}{60}$$

Express 1657900\times \frac{\sqrt{10}}{60} as a single fraction.

$$\frac{1657900\sqrt{10}}{60}$$

Divide 1657900\sqrt{10} by 60 to get \frac{82895}{3}\sqrt{10}.

$$\frac{82895}{3}\sqrt{10}$$