Solve sqrt{(4^2+3^3)^3}+18

$$\sqrt { ( 4 ^ { 2 } + 3 ^ { 3 } ) ^ { 3 } } + 18$$

Evaluate

$$43\sqrt{43}+18\approx 299.969856545$$

Solution Steps

Calculate 4 to the power of 2 and get 16.

$$\sqrt{\left(16+3^{3}\right)^{3}}+18$$

Calculate 3 to the power of 3 and get 27.

$$\sqrt{\left(16+27\right)^{3}}+18$$

Add 16 and 27 to get 43.

$$\sqrt{43^{3}}+18$$

Calculate 43 to the power of 3 and get 79507.

$$\sqrt{79507}+18$$

Factor 79507=43^{2}\times 43. Rewrite the square root of the product \sqrt{43^{2}\times 43} as the product of square roots \sqrt{43^{2}}\sqrt{43}. Take the square root of 43^{2}.

$$43\sqrt{43}+18$$