Solve 3sqrt{3}*(sqrt{12}-3sqrt{72})

$$3 \sqrt { 3 } \times ( \sqrt { 12 } - 3 \sqrt { 72 } )$$

Evaluate

$$18-54\sqrt{6}\approx -114.27244611$$

Solution Steps

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}.

$$3\sqrt{3}\left(2\sqrt{3}-3\sqrt{72}\right)$$

Factor 72=6^{2}\times 2. Rewrite the square root of the product \sqrt{6^{2}\times 2} as the product of square roots \sqrt{6^{2}}\sqrt{2}. Take the square root of 6^{2}.

$$3\sqrt{3}\left(2\sqrt{3}-3\times 6\sqrt{2}\right)$$

Multiply -3 and 6 to get -18.

$$3\sqrt{3}\left(2\sqrt{3}-18\sqrt{2}\right)$$

Use the distributive property to multiply 3\sqrt{3} by 2\sqrt{3}-18\sqrt{2}.

$$6\left(\sqrt{3}\right)^{2}-54\sqrt{3}\sqrt{2}$$

The square of \sqrt{3} is 3.

$$6\times 3-54\sqrt{3}\sqrt{2}$$

Multiply 6 and 3 to get 18.

$$18-54\sqrt{3}\sqrt{2}$$

To multiply \sqrt{3} and \sqrt{2}, multiply the numbers under the square root.

$$18-54\sqrt{6}$$