Solve sqrt{6^2+10^2-12%2^2+(7-9)4}

$$\sqrt{ { 6 }^{ 2 } + { 10 }^{ 2 } -12 \% { 2 }^{ 2 } +(7-9)4 }$$

Evaluate

$$\frac{2\sqrt{797}}{5}\approx 11.292475371$$

Solution Steps

Calculate 6 to the power of 2 and get 36.

$$\sqrt{36+10^{2}-\frac{12}{100}\times 2^{2}+\left(7-9\right)\times 4}$$

Calculate 10 to the power of 2 and get 100.

$$\sqrt{36+100-\frac{12}{100}\times 2^{2}+\left(7-9\right)\times 4}$$

Add 36 and 100 to get 136.

$$\sqrt{136-\frac{12}{100}\times 2^{2}+\left(7-9\right)\times 4}$$

Reduce the fraction \frac{12}{100} to lowest terms by extracting and canceling out 4.

$$\sqrt{136-\frac{3}{25}\times 2^{2}+\left(7-9\right)\times 4}$$

Calculate 2 to the power of 2 and get 4.

$$\sqrt{136-\frac{3}{25}\times 4+\left(7-9\right)\times 4}$$

Express \frac{3}{25}\times 4 as a single fraction.

$$\sqrt{136-\frac{3\times 4}{25}+\left(7-9\right)\times 4}$$

Multiply 3 and 4 to get 12.

$$\sqrt{136-\frac{12}{25}+\left(7-9\right)\times 4}$$

Convert 136 to fraction \frac{3400}{25}.

$$\sqrt{\frac{3400}{25}-\frac{12}{25}+\left(7-9\right)\times 4}$$

Since \frac{3400}{25} and \frac{12}{25} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{3400-12}{25}+\left(7-9\right)\times 4}$$

Subtract 12 from 3400 to get 3388.

$$\sqrt{\frac{3388}{25}+\left(7-9\right)\times 4}$$

Subtract 9 from 7 to get -2.

$$\sqrt{\frac{3388}{25}-2\times 4}$$

Multiply -2 and 4 to get -8.

$$\sqrt{\frac{3388}{25}-8}$$

Convert 8 to fraction \frac{200}{25}.

$$\sqrt{\frac{3388}{25}-\frac{200}{25}}$$

Since \frac{3388}{25} and \frac{200}{25} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{3388-200}{25}}$$

Subtract 200 from 3388 to get 3188.

$$\sqrt{\frac{3188}{25}}$$

Rewrite the square root of the division \sqrt{\frac{3188}{25}} as the division of square roots \frac{\sqrt{3188}}{\sqrt{25}}.

$$\frac{\sqrt{3188}}{\sqrt{25}}$$

Factor 3188=2^{2}\times 797. Rewrite the square root of the product \sqrt{2^{2}\times 797} as the product of square roots \sqrt{2^{2}}\sqrt{797}. Take the square root of 2^{2}.

$$\frac{2\sqrt{797}}{\sqrt{25}}$$

Calculate the square root of 25 and get 5.

$$\frac{2\sqrt{797}}{5}$$