Solve sqrt{5(7-5)^2-4}+3^2(2^3-5)

$$\sqrt { 5 ( 7 - 5 ) ^ { 2 } - 4 } + 3 ^ { 2 } ( 2 ^ { 3 } - 5 )$$

Evaluate

$$31$$

Solution Steps

Subtract 5 from 7 to get 2.

$$\sqrt{5\times 2^{2}-4}+3^{2}\left(2^{3}-5\right)$$

Calculate 2 to the power of 2 and get 4.

$$\sqrt{5\times 4-4}+3^{2}\left(2^{3}-5\right)$$

Multiply 5 and 4 to get 20.

$$\sqrt{20-4}+3^{2}\left(2^{3}-5\right)$$

Subtract 4 from 20 to get 16.

$$\sqrt{16}+3^{2}\left(2^{3}-5\right)$$

Calculate the square root of 16 and get 4.

$$4+3^{2}\left(2^{3}-5\right)$$

Calculate 3 to the power of 2 and get 9.

$$4+9\left(2^{3}-5\right)$$

Calculate 2 to the power of 3 and get 8.

$$4+9\left(8-5\right)$$

Subtract 5 from 8 to get 3.

$$4+9\times 3$$

Multiply 9 and 3 to get 27.

$$4+27$$

Add 4 and 27 to get 31.

$$31$$

Factor

$$31$$