Solve 2sqrt{8}*sqrt{18}

$$2 \sqrt { 8 } \cdot \sqrt { 18 }$$

Evaluate

$$24$$

Solution Steps

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}.

$$2\times 2\sqrt{2}\sqrt{18}$$

Multiply 2 and 2 to get 4.

$$4\sqrt{2}\sqrt{18}$$

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}.

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

Multiply 4 and 3 to get 12.

$$12\sqrt{2}\sqrt{2}$$

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

$$12\times 2$$

Multiply 12 and 2 to get 24.

$$24$$

Factor

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