Solve sqrt{100/63}

$$\sqrt { \frac { 100 } { 63 } }$$

Evaluate

$$\frac{10\sqrt{7}}{21}\approx 1.259881577$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{100}{63}} as the division of square roots \frac{\sqrt{100}}{\sqrt{63}}.

$$\frac{\sqrt{100}}{\sqrt{63}}$$

Calculate the square root of 100 and get 10.

$$\frac{10}{\sqrt{63}}$$

Factor 63=3^{2}\times 7. Rewrite the square root of the product \sqrt{3^{2}\times 7} as the product of square roots \sqrt{3^{2}}\sqrt{7}. Take the square root of 3^{2}.

$$\frac{10}{3\sqrt{7}}$$

Rationalize the denominator of \frac{10}{3\sqrt{7}} by multiplying numerator and denominator by \sqrt{7}.

$$\frac{10\sqrt{7}}{3\left(\sqrt{7}\right)^{2}}$$

The square of \sqrt{7} is 7.

$$\frac{10\sqrt{7}}{3\times 7}$$

Multiply 3 and 7 to get 21.

$$\frac{10\sqrt{7}}{21}$$