Solve sqrt{18}sqrt{24}=

$$\sqrt { 18 } \sqrt { 24 } =$$

Evaluate

$$12\sqrt{3}\approx 20.784609691$$

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}.

$$3\sqrt{2}\sqrt{24}$$

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}.

$$3\sqrt{2}\times 2\sqrt{6}$$

Multiply 3 and 2 to get 6.

$$6\sqrt{2}\sqrt{6}$$

Factor 6=2\times 3. Rewrite the square root of the product \sqrt{2\times 3} as the product of square roots \sqrt{2}\sqrt{3}.

$$6\sqrt{2}\sqrt{2}\sqrt{3}$$

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$6\times 2\sqrt{3}$$

Multiply 6 and 2 to get 12.

$$12\sqrt{3}$$