Solve -3sqrt{8}(sqrt{27})

$$-3 \sqrt{ 8 } ( \sqrt{ 27 } )$$

Evaluate

$$-18\sqrt{6}\approx -44.09081537$$

Solution Steps

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

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

Multiply -3 and 2 to get -6.

$$-6\sqrt{2}\sqrt{27}$$

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}.

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

Multiply -6 and 3 to get -18.

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

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

$$-18\sqrt{6}$$