Solve -sqrt{18}*sqrt{30}*sqrt{7}

$$- \sqrt { 18 } \cdot \sqrt { 30 } \cdot \sqrt { 7 }$$

Evaluate

$$-6\sqrt{105}\approx -61.481704596$$

Solution Steps

Factor 18=3^{2}\times 2. Rewrite the square root of the product \sqrt{3^{2}\times 2} as the product of square roots \sqrt{3^{2}}\sqrt{2}. Take the square root of 3^{2}.

$$\left(-3\sqrt{2}\right)\sqrt{30}\sqrt{7}$$

To multiply \sqrt{30} and \sqrt{7}, multiply the numbers under the square root.

$$\left(-3\sqrt{2}\right)\sqrt{210}$$

Multiply -1 and 3 to get -3.

$$-3\sqrt{2}\sqrt{210}$$

Factor 210=2\times 105. Rewrite the square root of the product \sqrt{2\times 105} as the product of square roots \sqrt{2}\sqrt{105}.

$$-3\sqrt{2}\sqrt{2}\sqrt{105}$$

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

$$-3\times 2\sqrt{105}$$

Multiply -3 and 2 to get -6.

$$-6\sqrt{105}$$