Solve 4sqrt{1/2}+3sqrt{1/3}-5

$$4 \sqrt { \frac { 1 } { 2 } } + 3 \sqrt { \frac { 1 } { 3 } } - 5$$

Evaluate

$$\sqrt{3}+2\sqrt{2}-5\approx -0.439522068$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{1}{2}} as the division of square roots \frac{\sqrt{1}}{\sqrt{2}}.

$$4\times \frac{\sqrt{1}}{\sqrt{2}}+3\sqrt{\frac{1}{3}}-5$$

Calculate the square root of 1 and get 1.

$$4\times \frac{1}{\sqrt{2}}+3\sqrt{\frac{1}{3}}-5$$

Rationalize the denominator of \frac{1}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$4\times \frac{\sqrt{2}}{\left(\sqrt{2}\right)^{2}}+3\sqrt{\frac{1}{3}}-5$$

The square of \sqrt{2} is 2.

$$4\times \frac{\sqrt{2}}{2}+3\sqrt{\frac{1}{3}}-5$$

Cancel out 2, the greatest common factor in 4 and 2.

$$2\sqrt{2}+3\sqrt{\frac{1}{3}}-5$$

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

$$2\sqrt{2}+3\times \frac{\sqrt{1}}{\sqrt{3}}-5$$

Calculate the square root of 1 and get 1.

$$2\sqrt{2}+3\times \frac{1}{\sqrt{3}}-5$$

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

$$2\sqrt{2}+3\times \frac{\sqrt{3}}{\left(\sqrt{3}\right)^{2}}-5$$

The square of \sqrt{3} is 3.

$$2\sqrt{2}+3\times \frac{\sqrt{3}}{3}-5$$

Cancel out 3 and 3.

$$2\sqrt{2}+\sqrt{3}-5$$