Solve sqrt{24}sqrt{27}=

$$\sqrt { 24 } \sqrt { 27 } =$$

Evaluate

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

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}.

$$2\sqrt{6}\sqrt{27}$$

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}.

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

Multiply 2 and 3 to get 6.

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

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

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

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

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

Multiply 6 and 3 to get 18.

$$18\sqrt{2}$$