Solve 2sqrt{75}-sqrt{27}+6sqrt{3/4}

$$2 \sqrt{ 75 } - \sqrt{ 27 } +6 \sqrt{ \frac{ 3 }{ 4 } }$$

Evaluate

$$10\sqrt{3}\approx 17.320508076$$

Solution Steps

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}.

$$2\times 5\sqrt{3}-\sqrt{27}+6\sqrt{\frac{3}{4}}$$

Multiply 2 and 5 to get 10.

$$10\sqrt{3}-\sqrt{27}+6\sqrt{\frac{3}{4}}$$

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}.

$$10\sqrt{3}-3\sqrt{3}+6\sqrt{\frac{3}{4}}$$

Combine 10\sqrt{3} and -3\sqrt{3} to get 7\sqrt{3}.

$$7\sqrt{3}+6\sqrt{\frac{3}{4}}$$

Rewrite the square root of the division \sqrt{\frac{3}{4}} as the division of square roots \frac{\sqrt{3}}{\sqrt{4}}.

$$7\sqrt{3}+6\times \frac{\sqrt{3}}{\sqrt{4}}$$

Calculate the square root of 4 and get 2.

$$7\sqrt{3}+6\times \frac{\sqrt{3}}{2}$$

Cancel out 2, the greatest common factor in 6 and 2.

$$7\sqrt{3}+3\sqrt{3}$$

Combine 7\sqrt{3} and 3\sqrt{3} to get 10\sqrt{3}.

$$10\sqrt{3}$$