Solve sqrt{6^{2}-(6^2+7^2-5^2/2*7)^2}

$$\sqrt { 6 ^ { 2 } - ( \frac { 6 ^ { 2 } + 7 ^ { 2 } - 5 ^ { 2 } } { 2 \times 7 } ) ^ { 2 } }$$

Evaluate

$$\frac{12\sqrt{6}}{7}\approx 4.199125273$$

Solution Steps

Calculate 6 to the power of 2 and get 36.

$$\sqrt{36-\left(\frac{6^{2}+7^{2}-5^{2}}{2\times 7}\right)^{2}}$$

Calculate 6 to the power of 2 and get 36.

$$\sqrt{36-\left(\frac{36+7^{2}-5^{2}}{2\times 7}\right)^{2}}$$

Calculate 7 to the power of 2 and get 49.

$$\sqrt{36-\left(\frac{36+49-5^{2}}{2\times 7}\right)^{2}}$$

Add 36 and 49 to get 85.

$$\sqrt{36-\left(\frac{85-5^{2}}{2\times 7}\right)^{2}}$$

Calculate 5 to the power of 2 and get 25.

$$\sqrt{36-\left(\frac{85-25}{2\times 7}\right)^{2}}$$

Subtract 25 from 85 to get 60.

$$\sqrt{36-\left(\frac{60}{2\times 7}\right)^{2}}$$

Multiply 2 and 7 to get 14.

$$\sqrt{36-\left(\frac{60}{14}\right)^{2}}$$

Reduce the fraction \frac{60}{14} to lowest terms by extracting and canceling out 2.

$$\sqrt{36-\left(\frac{30}{7}\right)^{2}}$$

Calculate \frac{30}{7} to the power of 2 and get \frac{900}{49}.

$$\sqrt{36-\frac{900}{49}}$$

Subtract \frac{900}{49} from 36 to get \frac{864}{49}.

$$\sqrt{\frac{864}{49}}$$

Rewrite the square root of the division \sqrt{\frac{864}{49}} as the division of square roots \frac{\sqrt{864}}{\sqrt{49}}.

$$\frac{\sqrt{864}}{\sqrt{49}}$$

Factor 864=12^{2}\times 6. Rewrite the square root of the product \sqrt{12^{2}\times 6} as the product of square roots \sqrt{12^{2}}\sqrt{6}. Take the square root of 12^{2}.

$$\frac{12\sqrt{6}}{\sqrt{49}}$$

Calculate the square root of 49 and get 7.

$$\frac{12\sqrt{6}}{7}$$