Solve 9sqrt{27}-2sqrt{12}

$$9 \sqrt { 27 } - 2 \sqrt { 12 }$$

Evaluate

$$23\sqrt{3}\approx 39.837168574$$

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}.

$$9\times 3\sqrt{3}-2\sqrt{12}$$

Multiply 9 and 3 to get 27.

$$27\sqrt{3}-2\sqrt{12}$$

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

$$27\sqrt{3}-2\times 2\sqrt{3}$$

Multiply -2 and 2 to get -4.

$$27\sqrt{3}-4\sqrt{3}$$

Combine 27\sqrt{3} and -4\sqrt{3} to get 23\sqrt{3}.

$$23\sqrt{3}$$