Solve frac{5sqrt{7}}{sqrt{35}}

$$\frac { 5 \sqrt { 7 } } { \sqrt { 35 } }$$

Evaluate

$$\sqrt{5}\approx 2.236067977$$

Solution Steps

Rationalize the denominator of \frac{5\sqrt{7}}{\sqrt{35}} by multiplying numerator and denominator by \sqrt{35}.

$$\frac{5\sqrt{7}\sqrt{35}}{\left(\sqrt{35}\right)^{2}}$$

The square of \sqrt{35} is 35.

$$\frac{5\sqrt{7}\sqrt{35}}{35}$$

Factor 35=7\times 5. Rewrite the square root of the product \sqrt{7\times 5} as the product of square roots \sqrt{7}\sqrt{5}.

$$\frac{5\sqrt{7}\sqrt{7}\sqrt{5}}{35}$$

Multiply \sqrt{7} and \sqrt{7} to get 7.

$$\frac{5\times 7\sqrt{5}}{35}$$

Multiply 5 and 7 to get 35.

$$\frac{35\sqrt{5}}{35}$$

Cancel out 35 and 35.

$$\sqrt{5}$$