Solve sqrt{64+25/40}

$$\sqrt { \frac { 64 + 25 } { 40 } }$$

Evaluate

$$\frac{\sqrt{890}}{20}\approx 1.491643389$$

Solution Steps

Add 64 and 25 to get 89.

$$\sqrt{\frac{89}{40}}$$

Rewrite the square root of the division \sqrt{\frac{89}{40}} as the division of square roots \frac{\sqrt{89}}{\sqrt{40}}.

$$\frac{\sqrt{89}}{\sqrt{40}}$$

Factor 40=2^{2}\times 10. Rewrite the square root of the product \sqrt{2^{2}\times 10} as the product of square roots \sqrt{2^{2}}\sqrt{10}. Take the square root of 2^{2}.

$$\frac{\sqrt{89}}{2\sqrt{10}}$$

Rationalize the denominator of \frac{\sqrt{89}}{2\sqrt{10}} by multiplying numerator and denominator by \sqrt{10}.

$$\frac{\sqrt{89}\sqrt{10}}{2\left(\sqrt{10}\right)^{2}}$$

The square of \sqrt{10} is 10.

$$\frac{\sqrt{89}\sqrt{10}}{2\times 10}$$

To multiply \sqrt{89} and \sqrt{10}, multiply the numbers under the square root.

$$\frac{\sqrt{890}}{2\times 10}$$

Multiply 2 and 10 to get 20.

$$\frac{\sqrt{890}}{20}$$