Solve =2sqrt{1/3}?sqrt{9}quadsqrt{12}+sqrt[3]{7/8-1}

$$= 2 \sqrt { \frac { 1 } { 3 } } ? \sqrt { 9 } \quad \sqrt { 12 } + \sqrt[ 3 ] { \frac { 7 } { 8 } - 1 }$$

Evaluate

$$\frac{23}{2}=11.5$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{1}{3}} as the division of square roots \frac{\sqrt{1}}{\sqrt{3}}.

$$2\times \frac{\sqrt{1}}{\sqrt{3}}\sqrt{9}\sqrt{12}+\sqrt[3]{\frac{7}{8}-1}$$

Calculate the square root of 1 and get 1.

$$2\times \frac{1}{\sqrt{3}}\sqrt{9}\sqrt{12}+\sqrt[3]{\frac{7}{8}-1}$$

Rationalize the denominator of \frac{1}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$2\times \frac{\sqrt{3}}{\left(\sqrt{3}\right)^{2}}\sqrt{9}\sqrt{12}+\sqrt[3]{\frac{7}{8}-1}$$

The square of \sqrt{3} is 3.

$$2\times \frac{\sqrt{3}}{3}\sqrt{9}\sqrt{12}+\sqrt[3]{\frac{7}{8}-1}$$

Calculate the square root of 9 and get 3.

$$2\times \frac{\sqrt{3}}{3}\times 3\sqrt{12}+\sqrt[3]{\frac{7}{8}-1}$$

Multiply 2 and 3 to get 6.

$$6\times \frac{\sqrt{3}}{3}\sqrt{12}+\sqrt[3]{\frac{7}{8}-1}$$

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}.

$$6\times \frac{\sqrt{3}}{3}\times 2\sqrt{3}+\sqrt[3]{\frac{7}{8}-1}$$

Multiply 6 and 2 to get 12.

$$12\times \frac{\sqrt{3}}{3}\sqrt{3}+\sqrt[3]{\frac{7}{8}-1}$$

Cancel out 3, the greatest common factor in 12 and 3.

$$4\sqrt{3}\sqrt{3}+\sqrt[3]{\frac{7}{8}-1}$$

Subtract 1 from \frac{7}{8} to get -\frac{1}{8}.

$$4\sqrt{3}\sqrt{3}+\sqrt[3]{-\frac{1}{8}}$$

Calculate \sqrt[3]{-\frac{1}{8}} and get -\frac{1}{2}.

$$4\sqrt{3}\sqrt{3}-\frac{1}{2}$$

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$4\times 3-\frac{1}{2}$$

Multiply 4 and 3 to get 12.

$$12-\frac{1}{2}$$

Subtract \frac{1}{2} from 12 to get \frac{23}{2}.

$$\frac{23}{2}$$

Factor

$$\frac{23}{2} = 11\frac{1}{2} = 11.5$$