Solve frac{2*sqrt{343}+sqrt{125}}{sqrt{5}}

$$\frac { 2 \cdot \sqrt { 343 } + \sqrt { 125 } } { \sqrt { 5 } }$$

Evaluate

$$\frac{14\sqrt{35}}{5}+5\approx 21.565023393$$

Solution Steps

Factor 343=7^{2}\times 7. Rewrite the square root of the product \sqrt{7^{2}\times 7} as the product of square roots \sqrt{7^{2}}\sqrt{7}. Take the square root of 7^{2}.

$$\frac{2\times 7\sqrt{7}+\sqrt{125}}{\sqrt{5}}$$

Multiply 2 and 7 to get 14.

$$\frac{14\sqrt{7}+\sqrt{125}}{\sqrt{5}}$$

Factor 125=5^{2}\times 5. Rewrite the square root of the product \sqrt{5^{2}\times 5} as the product of square roots \sqrt{5^{2}}\sqrt{5}. Take the square root of 5^{2}.

$$\frac{14\sqrt{7}+5\sqrt{5}}{\sqrt{5}}$$

Rationalize the denominator of \frac{14\sqrt{7}+5\sqrt{5}}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{\left(14\sqrt{7}+5\sqrt{5}\right)\sqrt{5}}{\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{\left(14\sqrt{7}+5\sqrt{5}\right)\sqrt{5}}{5}$$

Use the distributive property to multiply 14\sqrt{7}+5\sqrt{5} by \sqrt{5}.

$$\frac{14\sqrt{7}\sqrt{5}+5\left(\sqrt{5}\right)^{2}}{5}$$

To multiply \sqrt{7} and \sqrt{5}, multiply the numbers under the square root.

$$\frac{14\sqrt{35}+5\left(\sqrt{5}\right)^{2}}{5}$$

The square of \sqrt{5} is 5.

$$\frac{14\sqrt{35}+5\times 5}{5}$$

Multiply 5 and 5 to get 25.

$$\frac{14\sqrt{35}+25}{5}$$