Solve 2sqrt{27}+sqrt{75}

$$2 \sqrt { 27 } + \sqrt { 75 }$$

Evaluate

$$11\sqrt{3}\approx 19.052558883$$

Solution Steps

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}.

$$2\times 3\sqrt{3}+\sqrt{75}$$

Multiply 2 and 3 to get 6.

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

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 11\sqrt{3}.

$$11\sqrt{3}$$