Solve sqrt{((178*85)div3600}=

$$\sqrt{ ((178 \times 85) \div 3600 } =$$

Evaluate

$$\frac{\sqrt{15130}}{60}\approx 2.05006775$$

Solution Steps

Multiply 178 and 85 to get 15130.

$$\sqrt{\frac{15130}{3600}}$$

Reduce the fraction \frac{15130}{3600} to lowest terms by extracting and canceling out 10.

$$\sqrt{\frac{1513}{360}}$$

Rewrite the square root of the division \sqrt{\frac{1513}{360}} as the division of square roots \frac{\sqrt{1513}}{\sqrt{360}}.

$$\frac{\sqrt{1513}}{\sqrt{360}}$$

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}.

$$\frac{\sqrt{1513}}{6\sqrt{10}}$$

Rationalize the denominator of \frac{\sqrt{1513}}{6\sqrt{10}} by multiplying numerator and denominator by \sqrt{10}.

$$\frac{\sqrt{1513}\sqrt{10}}{6\left(\sqrt{10}\right)^{2}}$$

The square of \sqrt{10} is 10.

$$\frac{\sqrt{1513}\sqrt{10}}{6\times 10}$$

To multiply \sqrt{1513} and \sqrt{10}, multiply the numbers under the square root.

$$\frac{\sqrt{15130}}{6\times 10}$$

Multiply 6 and 10 to get 60.

$$\frac{\sqrt{15130}}{60}$$