Solve frac{sqrt{56^2-46^2}}{0.25*sqrt{10}}

$$\frac { \sqrt { 56 ^ { 2 } - 46 ^ { 2 } } } { 0.25 \cdot \sqrt { 10 } }$$

Evaluate

$$4\sqrt{102}\approx 40.398019753$$

Solution Steps

Calculate 56 to the power of 2 and get 3136.

$$\frac{\sqrt{3136-46^{2}}}{0.25\sqrt{10}}$$

Calculate 46 to the power of 2 and get 2116.

$$\frac{\sqrt{3136-2116}}{0.25\sqrt{10}}$$

Subtract 2116 from 3136 to get 1020.

$$\frac{\sqrt{1020}}{0.25\sqrt{10}}$$

Factor 1020=2^{2}\times 255. Rewrite the square root of the product \sqrt{2^{2}\times 255} as the product of square roots \sqrt{2^{2}}\sqrt{255}. Take the square root of 2^{2}.

$$\frac{2\sqrt{255}}{0.25\sqrt{10}}$$

Rationalize the denominator of \frac{2\sqrt{255}}{0.25\sqrt{10}} by multiplying numerator and denominator by \sqrt{10}.

$$\frac{2\sqrt{255}\sqrt{10}}{0.25\left(\sqrt{10}\right)^{2}}$$

The square of \sqrt{10} is 10.

$$\frac{2\sqrt{255}\sqrt{10}}{0.25\times 10}$$

To multiply \sqrt{255} and \sqrt{10}, multiply the numbers under the square root.

$$\frac{2\sqrt{2550}}{0.25\times 10}$$

Multiply 0.25 and 10 to get 2.5.

$$\frac{2\sqrt{2550}}{2.5}$$

Factor 2550=5^{2}\times 102. Rewrite the square root of the product \sqrt{5^{2}\times 102} as the product of square roots \sqrt{5^{2}}\sqrt{102}. Take the square root of 5^{2}.

$$\frac{2\times 5\sqrt{102}}{2.5}$$

Multiply 2 and 5 to get 10.

$$\frac{10\sqrt{102}}{2.5}$$

Divide 10\sqrt{102} by 2.5 to get 4\sqrt{102}.

$$4\sqrt{102}$$