Solve -sqrt{72}*sqrt{56}

$$- \sqrt { 72 } \times \sqrt { 56 }$$

Evaluate

$$-24\sqrt{7}\approx -63.498031466$$

Solution Steps

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}.

$$\left(-6\sqrt{2}\right)\sqrt{56}$$

Factor 56=2^{2}\times 14. Rewrite the square root of the product \sqrt{2^{2}\times 14} as the product of square roots \sqrt{2^{2}}\sqrt{14}. Take the square root of 2^{2}.

$$\left(-6\sqrt{2}\right)\times 2\sqrt{14}$$

Multiply -1 and 6 to get -6.

$$-6\sqrt{2}\times 2\sqrt{14}$$

Multiply -6 and 2 to get -12.

$$-12\sqrt{2}\sqrt{14}$$

Factor 14=2\times 7. Rewrite the square root of the product \sqrt{2\times 7} as the product of square roots \sqrt{2}\sqrt{7}.

$$-12\sqrt{2}\sqrt{2}\sqrt{7}$$

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$-12\times 2\sqrt{7}$$

Multiply -12 and 2 to get -24.

$$-24\sqrt{7}$$