Solve 3sqrt{75}+5sqrt{3}-sqrt{27}

$$3 \sqrt { 75 } + 5 \sqrt { 3 } - \sqrt { 27 }$$

Evaluate

$$17\sqrt{3}\approx 29.444863729$$

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}.

$$3\times 5\sqrt{3}+5\sqrt{3}-\sqrt{27}$$

Multiply 3 and 5 to get 15.

$$15\sqrt{3}+5\sqrt{3}-\sqrt{27}$$

Combine 15\sqrt{3} and 5\sqrt{3} to get 20\sqrt{3}.

$$20\sqrt{3}-\sqrt{27}$$

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}.

$$20\sqrt{3}-3\sqrt{3}$$

Combine 20\sqrt{3} and -3\sqrt{3} to get 17\sqrt{3}.

$$17\sqrt{3}$$