Solve 4sqrt[]{1/2}+3sqrt{1/3}-sqrt{8}

$$4 \sqrt[ ]{ \frac{ 1 }{ 2 } } +3 \sqrt{ \frac{ 1 }{ 3 } } - \sqrt{ 8 }$$

Evaluate

$$\sqrt{3}\approx 1.732050808$$

Solution Steps

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

$$4\sqrt[2]{\frac{1}{2}}+3\times \frac{\sqrt{1}}{\sqrt{3}}-\sqrt{8}$$

Calculate the square root of 1 and get 1.

$$4\sqrt[2]{\frac{1}{2}}+3\times \frac{1}{\sqrt{3}}-\sqrt{8}$$

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

$$4\sqrt[2]{\frac{1}{2}}+3\times \frac{\sqrt{3}}{\left(\sqrt{3}\right)^{2}}-\sqrt{8}$$

The square of \sqrt{3} is 3.

$$4\sqrt[2]{\frac{1}{2}}+3\times \frac{\sqrt{3}}{3}-\sqrt{8}$$

Cancel out 3 and 3.

$$4\sqrt[2]{\frac{1}{2}}+\sqrt{3}-\sqrt{8}$$

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$4\sqrt[2]{\frac{1}{2}}+\sqrt{3}-2\sqrt{2}$$