Solve 5sqrt{27}-2sqrt{75}+3sqrt{3}=

$$5 \sqrt { 27 } - 2 \sqrt { 75 } + 3 \sqrt { 3 } =$$

Evaluate

$$8\sqrt{3}\approx 13.856406461$$

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}.

$$5\times 3\sqrt{3}-2\sqrt{75}+3\sqrt{3}$$

Multiply 5 and 3 to get 15.

$$15\sqrt{3}-2\sqrt{75}+3\sqrt{3}$$

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}.

$$15\sqrt{3}-2\times 5\sqrt{3}+3\sqrt{3}$$

Multiply -2 and 5 to get -10.

$$15\sqrt{3}-10\sqrt{3}+3\sqrt{3}$$

Combine 15\sqrt{3} and -10\sqrt{3} to get 5\sqrt{3}.

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

Combine 5\sqrt{3} and 3\sqrt{3} to get 8\sqrt{3}.

$$8\sqrt{3}$$