Solve sqrt{153/175}

$$\sqrt { \frac { 153 } { 175 } }$$

Evaluate

$$\frac{3\sqrt{119}}{35}\approx 0.935032467$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{153}{175}} as the division of square roots \frac{\sqrt{153}}{\sqrt{175}}.

$$\frac{\sqrt{153}}{\sqrt{175}}$$

Factor 153=3^{2}\times 17. Rewrite the square root of the product \sqrt{3^{2}\times 17} as the product of square roots \sqrt{3^{2}}\sqrt{17}. Take the square root of 3^{2}.

$$\frac{3\sqrt{17}}{\sqrt{175}}$$

Factor 175=5^{2}\times 7. Rewrite the square root of the product \sqrt{5^{2}\times 7} as the product of square roots \sqrt{5^{2}}\sqrt{7}. Take the square root of 5^{2}.

$$\frac{3\sqrt{17}}{5\sqrt{7}}$$

Rationalize the denominator of \frac{3\sqrt{17}}{5\sqrt{7}} by multiplying numerator and denominator by \sqrt{7}.

$$\frac{3\sqrt{17}\sqrt{7}}{5\left(\sqrt{7}\right)^{2}}$$

The square of \sqrt{7} is 7.

$$\frac{3\sqrt{17}\sqrt{7}}{5\times 7}$$

To multiply \sqrt{17} and \sqrt{7}, multiply the numbers under the square root.

$$\frac{3\sqrt{119}}{5\times 7}$$

Multiply 5 and 7 to get 35.

$$\frac{3\sqrt{119}}{35}$$