Solve 3sqrt{24}*sqrt{3}=

$$3 \sqrt { 24 } \cdot \sqrt { 3 } =$$

Evaluate

$$18\sqrt{2}\approx 25.455844123$$

Solution Steps

Factor 24=3\times 8. Rewrite the square root of the product \sqrt{3\times 8} as the product of square roots \sqrt{3}\sqrt{8}.

$$3\sqrt{3}\sqrt{8}\sqrt{3}$$

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

$$3\times 3\sqrt{8}$$

Multiply 3 and 3 to get 9.

$$9\sqrt{8}$$

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$9\times 2\sqrt{2}$$

Multiply 9 and 2 to get 18.

$$18\sqrt{2}$$