Solve -sqrt{27}*sqrt{54}

$$- \sqrt{ 27 } \times \sqrt{ 54 }$$

Evaluate

$$-27\sqrt{2}\approx -38.183766184$$

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}.

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

Factor 54=3^{2}\times 6. Rewrite the square root of the product \sqrt{3^{2}\times 6} as the product of square roots \sqrt{3^{2}}\sqrt{6}. Take the square root of 3^{2}.

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

Multiply -1 and 3 to get -3.

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

Multiply -3 and 3 to get -9.

$$-9\sqrt{3}\sqrt{6}$$

Factor 6=3\times 2. Rewrite the square root of the product \sqrt{3\times 2} as the product of square roots \sqrt{3}\sqrt{2}.

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

Multiply \sqrt{3} and \sqrt{3} to get 3.

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

Multiply -9 and 3 to get -27.

$$-27\sqrt{2}$$