Solve 2sqrt{75}-4sqrt{27}+sqrt[3]{128}

$$2 \sqrt{ 75 } -4 \sqrt{ 27 } + \sqrt[ 3 ]{ 128 }$$

Evaluate

$$4\sqrt[3]{2}-2\sqrt{3}\approx 1.575582584$$

Solution Steps

Factor 75=5^{2}\times 3. Rewrite the square root of the product \sqrt{5^{2}\times 3} as the product of square roots \sqrt{5^{2}}\sqrt{3}. Take the square root of 5^{2}.

$$2\times 5\sqrt{3}-4\sqrt{27}+\sqrt[3]{128}$$

Multiply 2 and 5 to get 10.

$$10\sqrt{3}-4\sqrt{27}+\sqrt[3]{128}$$

Factor 27=3^{2}\times 3. Rewrite the square root of the product \sqrt{3^{2}\times 3} as the product of square roots \sqrt{3^{2}}\sqrt{3}. Take the square root of 3^{2}.

$$10\sqrt{3}-4\times 3\sqrt{3}+\sqrt[3]{128}$$

Multiply -4 and 3 to get -12.

$$10\sqrt{3}-12\sqrt{3}+\sqrt[3]{128}$$

Combine 10\sqrt{3} and -12\sqrt{3} to get -2\sqrt{3}.

$$-2\sqrt{3}+\sqrt[3]{128}$$