Solve sqrt{25^2-7^2/27}

$$\sqrt{ \frac{ { 25 }^{ 2 } - { 7 }^{ 2 } }{ 27 } }$$

Evaluate

$$\frac{8\sqrt{3}}{3}\approx 4.618802154$$

Solution Steps

Calculate 25 to the power of 2 and get 625.

$$\sqrt{\frac{625-7^{2}}{27}}$$

Calculate 7 to the power of 2 and get 49.

$$\sqrt{\frac{625-49}{27}}$$

Subtract 49 from 625 to get 576.

$$\sqrt{\frac{576}{27}}$$

Reduce the fraction \frac{576}{27} to lowest terms by extracting and canceling out 9.

$$\sqrt{\frac{64}{3}}$$

Rewrite the square root of the division \sqrt{\frac{64}{3}} as the division of square roots \frac{\sqrt{64}}{\sqrt{3}}.

$$\frac{\sqrt{64}}{\sqrt{3}}$$

Calculate the square root of 64 and get 8.

$$\frac{8}{\sqrt{3}}$$

Rationalize the denominator of \frac{8}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{8\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{8\sqrt{3}}{3}$$