Solve 5+sqrt[3]{(-8)^2}-(frac{sqrt{27}-sqrt{12}}{sqrt{3}}+2)]sqrt{7-1/4}

$$5 + \sqrt[ 3 ] { ( - 8 ) ^ { 2 } } - ( \frac { \sqrt { 27 } - \sqrt { 12 } } { \sqrt { 3 } } + 2 ) ] \sqrt { 7 - \frac { 1 } { 4 } }$$

Evaluate

$$6$$

Solution Steps

Calculate -8 to the power of 2 and get 64.

$$5+\sqrt[3]{64}-\left(\frac{\sqrt{27}-\sqrt{12}}{\sqrt{3}}+2\right)$$

Calculate \sqrt[3]{64} and get 4.

$$5+4-\left(\frac{\sqrt{27}-\sqrt{12}}{\sqrt{3}}+2\right)$$

Add 5 and 4 to get 9.

$$9-\left(\frac{\sqrt{27}-\sqrt{12}}{\sqrt{3}}+2\right)$$

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}.

$$9-\left(\frac{3\sqrt{3}-\sqrt{12}}{\sqrt{3}}+2\right)$$

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

$$9-\left(\frac{3\sqrt{3}-2\sqrt{3}}{\sqrt{3}}+2\right)$$

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

$$9-\left(\frac{\sqrt{3}}{\sqrt{3}}+2\right)$$

Rewrite the division of square roots \frac{\sqrt{3}}{\sqrt{3}} as the square root of the division \sqrt{\frac{3}{3}} and perform the division.

$$9-\left(\sqrt{1}+2\right)$$

Calculate the square root of 1 and get 1.

$$9-\left(1+2\right)$$

Add 1 and 2 to get 3.

$$9-3$$

Subtract 3 from 9 to get 6.

$$6$$

Factor

$$2\times 3$$