Solve sqrt{125/3.375}=

$$\sqrt{ \frac{ 125 }{ 3.375 } } =$$

Evaluate

$$\frac{10\sqrt{30}}{9}\approx 6.085806195$$

Solution Steps

Expand \frac{125}{3.375} by multiplying both numerator and the denominator by 1000.

$$\sqrt{\frac{125000}{3375}}$$

Reduce the fraction \frac{125000}{3375} to lowest terms by extracting and canceling out 125.

$$\sqrt{\frac{1000}{27}}$$

Rewrite the square root of the division \sqrt{\frac{1000}{27}} as the division of square roots \frac{\sqrt{1000}}{\sqrt{27}}.

$$\frac{\sqrt{1000}}{\sqrt{27}}$$

Factor 1000=10^{2}\times 10. Rewrite the square root of the product \sqrt{10^{2}\times 10} as the product of square roots \sqrt{10^{2}}\sqrt{10}. Take the square root of 10^{2}.

$$\frac{10\sqrt{10}}{\sqrt{27}}$$

Factor 27=3^{2}\times 3. Rewrite the square root of the product \sqrt{3^{2}\times 3} as the product of square roots \sqrt{3^{2}}\sqrt{3}. Take the square root of 3^{2}.

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

Rationalize the denominator of \frac{10\sqrt{10}}{3\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{10\sqrt{10}\sqrt{3}}{3\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

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

To multiply \sqrt{10} and \sqrt{3}, multiply the numbers under the square root.

$$\frac{10\sqrt{30}}{3\times 3}$$

Multiply 3 and 3 to get 9.

$$\frac{10\sqrt{30}}{9}$$