Solve 5^3^sqrt{8}-4sqrt{8}+9

$${ 5 }^{ { 3 }^{ } } \sqrt{ 8 } -4 \sqrt{ 8 } +9$$

Evaluate

$$242\sqrt{2}+9\approx 351.239682094$$

Solution Steps

Calculate 3 to the power of 1 and get 3.

$$5^{3}\sqrt{8}-4\sqrt{8}+9$$

Calculate 5 to the power of 3 and get 125.

$$125\sqrt{8}-4\sqrt{8}+9$$

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$125\times 2\sqrt{2}-4\sqrt{8}+9$$

Multiply 125 and 2 to get 250.

$$250\sqrt{2}-4\sqrt{8}+9$$

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$250\sqrt{2}-4\times 2\sqrt{2}+9$$

Multiply -4 and 2 to get -8.

$$250\sqrt{2}-8\sqrt{2}+9$$

Combine 250\sqrt{2} and -8\sqrt{2} to get 242\sqrt{2}.

$$242\sqrt{2}+9$$