Solve 3sqrt{24}*(-sqrt{42})

$$3 \sqrt{ 24 } \times (- \sqrt{ 42 } )$$

Evaluate

$$-36\sqrt{7}\approx -95.247047198$$

Solution Steps

Factor 24=2^{2}\times 6. Rewrite the square root of the product \sqrt{2^{2}\times 6} as the product of square roots \sqrt{2^{2}}\sqrt{6}. Take the square root of 2^{2}.

$$3\times 2\sqrt{6}\left(-\sqrt{42}\right)$$

Multiply 3 and 2 to get 6.

$$6\sqrt{6}\left(-\sqrt{42}\right)$$

Multiply 6 and -1 to get -6.

$$-6\sqrt{6}\sqrt{42}$$

Factor 42=6\times 7. Rewrite the square root of the product \sqrt{6\times 7} as the product of square roots \sqrt{6}\sqrt{7}.

$$-6\sqrt{6}\sqrt{6}\sqrt{7}$$

Multiply \sqrt{6} and \sqrt{6} to get 6.

$$-6\times 6\sqrt{7}$$

Multiply -6 and 6 to get -36.

$$-36\sqrt{7}$$