Solve 4^{2}+2+(2^4+5+2*5)+sqrt{1^3+3*(5^2-1-4^2)}

$$4 ^ { 2 } + 2 + ( 2 ^ { 4 } + 5 + 2 \times 5 ) + \sqrt { 1 ^ { 3 } + 3 \times ( 5 ^ { 2 } - 1 - 4 ^ { 2 } ) }$$

Evaluate

$$54$$

Solution Steps

Calculate 4 to the power of 2 and get 16.

$$16+2+2^{4}+5+2\times 5+\sqrt{1^{3}+3\left(5^{2}-1-4^{2}\right)}$$

Add 16 and 2 to get 18.

$$18+2^{4}+5+2\times 5+\sqrt{1^{3}+3\left(5^{2}-1-4^{2}\right)}$$

Calculate 2 to the power of 4 and get 16.

$$18+16+5+2\times 5+\sqrt{1^{3}+3\left(5^{2}-1-4^{2}\right)}$$

Add 18 and 16 to get 34.

$$34+5+2\times 5+\sqrt{1^{3}+3\left(5^{2}-1-4^{2}\right)}$$

Add 34 and 5 to get 39.

$$39+2\times 5+\sqrt{1^{3}+3\left(5^{2}-1-4^{2}\right)}$$

Multiply 2 and 5 to get 10.

$$39+10+\sqrt{1^{3}+3\left(5^{2}-1-4^{2}\right)}$$

Add 39 and 10 to get 49.

$$49+\sqrt{1^{3}+3\left(5^{2}-1-4^{2}\right)}$$

Calculate 1 to the power of 3 and get 1.

$$49+\sqrt{1+3\left(5^{2}-1-4^{2}\right)}$$

Calculate 5 to the power of 2 and get 25.

$$49+\sqrt{1+3\left(25-1-4^{2}\right)}$$

Subtract 1 from 25 to get 24.

$$49+\sqrt{1+3\left(24-4^{2}\right)}$$

Calculate 4 to the power of 2 and get 16.

$$49+\sqrt{1+3\left(24-16\right)}$$

Subtract 16 from 24 to get 8.

$$49+\sqrt{1+3\times 8}$$

Multiply 3 and 8 to get 24.

$$49+\sqrt{1+24}$$

Add 1 and 24 to get 25.

$$49+\sqrt{25}$$

Calculate the square root of 25 and get 5.

$$49+5$$

Add 49 and 5 to get 54.

$$54$$

Factor

$$2\times 3^{3}$$