Solve 5sqrt[3]{3}+5^3sqrt{24}-6sqrt[3]{81}

$$5 \sqrt[ 3 ] { 3 } + 5 ^ { 3 } \sqrt { 24 } - 6 \sqrt[ 3 ] { 81 }$$

Evaluate

$$250\sqrt{6}-13\sqrt[3]{3}\approx 593.623191282$$

Solution Steps

Calculate 5 to the power of 3 and get 125.

$$5\sqrt[3]{3}+125\sqrt{24}-6\sqrt[3]{81}$$

Factor 24=2^{2}\times 6. Rewrite the square root of the product \sqrt{2^{2}\times 6} as the product of square roots \sqrt{2^{2}}\sqrt{6}. Take the square root of 2^{2}.

$$5\sqrt[3]{3}+125\times 2\sqrt{6}-6\sqrt[3]{81}$$

Multiply 125 and 2 to get 250.

$$5\sqrt[3]{3}+250\sqrt{6}-6\sqrt[3]{81}$$