Solve sqrt{2}sqrt{8}sqrt{18}sqrt{32}

$$\sqrt { 2 } \sqrt { 8 } \sqrt { 18 } \sqrt { 32 }$$

Evaluate

$$96$$

Solution Steps

Factor 8=2\times 4. Rewrite the square root of the product \sqrt{2\times 4} as the product of square roots \sqrt{2}\sqrt{4}.

$$\sqrt{2}\sqrt{2}\sqrt{4}\sqrt{18}\sqrt{32}$$

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

$$2\sqrt{4}\sqrt{18}\sqrt{32}$$

Factor 32=4\times 8. Rewrite the square root of the product \sqrt{4\times 8} as the product of square roots \sqrt{4}\sqrt{8}.

$$2\sqrt{4}\sqrt{18}\sqrt{4}\sqrt{8}$$

Multiply \sqrt{4} and \sqrt{4} to get 4.

$$2\times 4\sqrt{18}\sqrt{8}$$

Multiply 2 and 4 to get 8.

$$8\sqrt{18}\sqrt{8}$$

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}.

$$8\times 3\sqrt{2}\sqrt{8}$$

Multiply 8 and 3 to get 24.

$$24\sqrt{2}\sqrt{8}$$

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}.

$$24\sqrt{2}\times 2\sqrt{2}$$

Multiply 24 and 2 to get 48.

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

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

$$48\times 2$$

Multiply 48 and 2 to get 96.

$$96$$

Factor

$$2^{5}\times 3$$