Solve -3sqrt{5}(2sqrt{5}+3sqrt{12})

$$- 3 \sqrt { 5 } ( 2 \sqrt { 5 } + 3 \sqrt { 12 } )$$

Evaluate

$$-18\sqrt{15}-30\approx -99.713700232$$

Solution Steps

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

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

Multiply 3 and 2 to get 6.

$$-3\sqrt{5}\left(2\sqrt{5}+6\sqrt{3}\right)$$

Use the distributive property to multiply -3\sqrt{5} by 2\sqrt{5}+6\sqrt{3}.

$$-6\left(\sqrt{5}\right)^{2}-18\sqrt{3}\sqrt{5}$$

The square of \sqrt{5} is 5.

$$-6\times 5-18\sqrt{3}\sqrt{5}$$

Multiply -6 and 5 to get -30.

$$-30-18\sqrt{3}\sqrt{5}$$

To multiply \sqrt{3} and \sqrt{5}, multiply the numbers under the square root.

$$-30-18\sqrt{15}$$