Solve sqrt{18*3}=sqrt{6*3*3}=

$$\sqrt { 18 \times 3 } = \sqrt { 6 \times 3 \times 3 } =$$

Verify

Solution Steps

Multiply 18 and 3 to get 54.

$$\sqrt{54}=\sqrt{6\times 3\times 3}$$

Factor 54=3^{2}\times 6. Rewrite the square root of the product \sqrt{3^{2}\times 6} as the product of square roots \sqrt{3^{2}}\sqrt{6}. Take the square root of 3^{2}.

$$3\sqrt{6}=\sqrt{6\times 3\times 3}$$

Multiply 6 and 3 to get 18.

$$3\sqrt{6}=\sqrt{18\times 3}$$

Multiply 18 and 3 to get 54.

$$3\sqrt{6}=\sqrt{54}$$

Factor 54=3^{2}\times 6. Rewrite the square root of the product \sqrt{3^{2}\times 6} as the product of square roots \sqrt{3^{2}}\sqrt{6}. Take the square root of 3^{2}.

$$3\sqrt{6}=3\sqrt{6}$$

Subtract 3\sqrt{6} from both sides.

$$3\sqrt{6}-3\sqrt{6}=0$$

Combine 3\sqrt{6} and -3\sqrt{6} to get 0.

$$0=0$$

Compare 0 and 0.

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