Solve sqrt{24}*sqrt{27}quadsqrt{6}*(-sqrt{15})

$$\sqrt { 24 } \times \sqrt { 27 } \quad \sqrt { 6 } \times ( - \sqrt { 15 } )$$

Evaluate

$$-108\sqrt{5}\approx -241.49534157$$

Solution Steps

Factor 24=6\times 4. Rewrite the square root of the product \sqrt{6\times 4} as the product of square roots \sqrt{6}\sqrt{4}.

$$\sqrt{6}\sqrt{4}\sqrt{27}\sqrt{6}\left(-\sqrt{15}\right)$$

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

$$6\sqrt{27}\sqrt{4}\left(-\sqrt{15}\right)$$

Factor 27=3^{2}\times 3. Rewrite the square root of the product \sqrt{3^{2}\times 3} as the product of square roots \sqrt{3^{2}}\sqrt{3}. Take the square root of 3^{2}.

$$6\times 3\sqrt{3}\sqrt{4}\left(-\sqrt{15}\right)$$

Multiply 6 and 3 to get 18.

$$18\sqrt{3}\sqrt{4}\left(-\sqrt{15}\right)$$

Calculate the square root of 4 and get 2.

$$18\sqrt{3}\times 2\left(-\sqrt{15}\right)$$

Multiply 18 and 2 to get 36.

$$36\sqrt{3}\left(-\sqrt{15}\right)$$

Multiply 36 and -1 to get -36.

$$-36\sqrt{3}\sqrt{15}$$

Factor 15=3\times 5. Rewrite the square root of the product \sqrt{3\times 5} as the product of square roots \sqrt{3}\sqrt{5}.

$$-36\sqrt{3}\sqrt{3}\sqrt{5}$$

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$-36\times 3\sqrt{5}$$

Multiply -36 and 3 to get -108.

$$-108\sqrt{5}$$