Solve sqrt{48}+6sqrt{1/3}-sqrt{75}

$$\sqrt { 48 } + 6 \sqrt { \frac { 1 } { 3 } } - \sqrt { 75 }$$

Evaluate

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

Solution Steps

Factor 48=4^{2}\times 3. Rewrite the square root of the product \sqrt{4^{2}\times 3} as the product of square roots \sqrt{4^{2}}\sqrt{3}. Take the square root of 4^{2}.

$$4\sqrt{3}+6\sqrt{\frac{1}{3}}-\sqrt{75}$$

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

$$4\sqrt{3}+6\times \frac{\sqrt{1}}{\sqrt{3}}-\sqrt{75}$$

Calculate the square root of 1 and get 1.

$$4\sqrt{3}+6\times \frac{1}{\sqrt{3}}-\sqrt{75}$$

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

$$4\sqrt{3}+6\times \frac{\sqrt{3}}{\left(\sqrt{3}\right)^{2}}-\sqrt{75}$$

The square of \sqrt{3} is 3.

$$4\sqrt{3}+6\times \frac{\sqrt{3}}{3}-\sqrt{75}$$

Cancel out 3, the greatest common factor in 6 and 3.

$$4\sqrt{3}+2\sqrt{3}-\sqrt{75}$$

Combine 4\sqrt{3} and 2\sqrt{3} to get 6\sqrt{3}.

$$6\sqrt{3}-\sqrt{75}$$

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}.

$$6\sqrt{3}-5\sqrt{3}$$

Combine 6\sqrt{3} and -5\sqrt{3} to get \sqrt{3}.

$$\sqrt{3}$$