Solve 2sqrt{6}*sqrt{8}=2sqrt{48}

$$2 \sqrt{ 6 } \times \sqrt{ 8 } =2 \sqrt{ 48 }$$

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Solution Steps

Cancel out 2 on both sides.

$$\sqrt{6}\sqrt{8}=\sqrt{48}$$

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}.

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

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}.

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

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

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

Factor 48=4^{2}\times 3. Rewrite the square root of the product \sqrt{4^{2}\times 3} as the product of square roots \sqrt{4^{2}}\sqrt{3}. Take the square root of 4^{2}.

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

Multiply 2 and 2 to get 4.

$$4\sqrt{3}=4\sqrt{3}$$

Subtract 4\sqrt{3} from both sides.

$$4\sqrt{3}-4\sqrt{3}=0$$

Combine 4\sqrt{3} and -4\sqrt{3} to get 0.

$$0=0$$

Compare 0 and 0.

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