Solve {l}{sqrt[3]{4}+sqrt[3]{99}}{+sqrt[3]{100}}{+sqrt{90}}{+3sqrt{1000}}

$$\left. \begin{array} { l } { \sqrt[ 3 ] { 4 } + \sqrt[ 3 ] { 99 } } \\ { + \sqrt[ 3 ] { 100 } } \\ { + \sqrt { 90 } } \\ { + 3 \sqrt { 1000 } } \end{array} \right.$$

Evaluate

$$\sqrt[3]{99}+33\sqrt{10}+2^{\frac{2}{3}}+10^{\frac{2}{3}}\approx 115.21021768$$

Solution Steps

Factor 90=3^{2}\times 10. Rewrite the square root of the product \sqrt{3^{2}\times 10} as the product of square roots \sqrt{3^{2}}\sqrt{10}. Take the square root of 3^{2}.

$$\sqrt[3]{4}+\sqrt[3]{99}+\sqrt[3]{100}+3\sqrt{10}+3\sqrt{1000}$$

Factor 1000=10^{2}\times 10. Rewrite the square root of the product \sqrt{10^{2}\times 10} as the product of square roots \sqrt{10^{2}}\sqrt{10}. Take the square root of 10^{2}.

$$\sqrt[3]{4}+\sqrt[3]{99}+\sqrt[3]{100}+3\sqrt{10}+3\times 10\sqrt{10}$$

Multiply 3 and 10 to get 30.

$$\sqrt[3]{4}+\sqrt[3]{99}+\sqrt[3]{100}+3\sqrt{10}+30\sqrt{10}$$

Combine 3\sqrt{10} and 30\sqrt{10} to get 33\sqrt{10}.

$$\sqrt[3]{4}+\sqrt[3]{99}+\sqrt[3]{100}+33\sqrt{10}$$