Solve sqrt{6}*sqrt{2}*sqrt{48}=

$$\sqrt { 6 } \times \sqrt { 2 } \times \sqrt { 48 } =$$

Evaluate

$$24$$

Solution Steps

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}.

$$\sqrt{2}\sqrt{3}\sqrt{2}\sqrt{48}$$

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

$$2\sqrt{3}\sqrt{48}$$

Factor 48=3\times 16. Rewrite the square root of the product \sqrt{3\times 16} as the product of square roots \sqrt{3}\sqrt{16}.

$$2\sqrt{3}\sqrt{3}\sqrt{16}$$

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

$$2\times 3\sqrt{16}$$

Multiply 2 and 3 to get 6.

$$6\sqrt{16}$$

Calculate the square root of 16 and get 4.

$$6\times 4$$

Multiply 6 and 4 to get 24.

$$24$$

Factor

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