Solve -3sqrt{2}(5sqrt{3}+7sqrt{18}

$$- 3 \sqrt { 2 } ( 5 \sqrt { 3 } + 7 \sqrt { 18 }$$

Evaluate

$$-15\sqrt{6}-126\approx -162.742346142$$

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}.

$$-3\sqrt{2}\left(5\sqrt{3}+7\times 3\sqrt{2}\right)$$

Multiply 7 and 3 to get 21.

$$-3\sqrt{2}\left(5\sqrt{3}+21\sqrt{2}\right)$$

Use the distributive property to multiply -3\sqrt{2} by 5\sqrt{3}+21\sqrt{2}.

$$-15\sqrt{3}\sqrt{2}-63\left(\sqrt{2}\right)^{2}$$

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

$$-15\sqrt{6}-63\left(\sqrt{2}\right)^{2}$$

The square of \sqrt{2} is 2.

$$-15\sqrt{6}-63\times 2$$

Multiply -63 and 2 to get -126.

$$-15\sqrt{6}-126$$