Solve sqrt{2*(5^2-3^2)+(7^2+5):27+2}

$$\sqrt { 2 \times ( 5 ^ { 2 } - 3 ^ { 2 } ) + ( 7 ^ { 2 } + 5 ) : 27 + 2 }$$

Evaluate

$$6$$

Solution Steps

Calculate 5 to the power of 2 and get 25.

$$\sqrt{2\left(25-3^{2}\right)+\frac{7^{2}+5}{27}+2}$$

Calculate 3 to the power of 2 and get 9.

$$\sqrt{2\left(25-9\right)+\frac{7^{2}+5}{27}+2}$$

Subtract 9 from 25 to get 16.

$$\sqrt{2\times 16+\frac{7^{2}+5}{27}+2}$$

Multiply 2 and 16 to get 32.

$$\sqrt{32+\frac{7^{2}+5}{27}+2}$$

Calculate 7 to the power of 2 and get 49.

$$\sqrt{32+\frac{49+5}{27}+2}$$

Add 49 and 5 to get 54.

$$\sqrt{32+\frac{54}{27}+2}$$

Divide 54 by 27 to get 2.

$$\sqrt{32+2+2}$$

Add 32 and 2 to get 34.

$$\sqrt{34+2}$$

Add 34 and 2 to get 36.

$$\sqrt{36}$$

Calculate the square root of 36 and get 6.

$$6$$

Factor

$$2\times 3$$