Solve sqrt{8}*sqrt{12}*sqrt{24}

$$\sqrt { 8 } \times \sqrt { 12 } \times \sqrt { 24 }$$

Evaluate

$$48$$

Solution Steps

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

$$\sqrt{8}\sqrt{12}\sqrt{8}\sqrt{3}$$

Multiply \sqrt{8} and \sqrt{8} to get 8.

$$8\sqrt{12}\sqrt{3}$$

Factor 12=3\times 4. Rewrite the square root of the product \sqrt{3\times 4} as the product of square roots \sqrt{3}\sqrt{4}.

$$8\sqrt{3}\sqrt{4}\sqrt{3}$$

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

$$8\times 3\sqrt{4}$$

Multiply 8 and 3 to get 24.

$$24\sqrt{4}$$

Calculate the square root of 4 and get 2.

$$24\times 2$$

Multiply 24 and 2 to get 48.

$$48$$

Factor

$$2^{4}\times 3$$