Solve sqrt{9+9}=sqrt{18}=3sqrt{2}

$$\sqrt { 9 + 9 } = \sqrt { 18 } = 3 \sqrt { 2 }$$

Verify

Solution Steps

Add 9 and 9 to get 18.

$$\sqrt{18}=\sqrt{18}\text{ and }\sqrt{18}=3\sqrt{2}$$

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}.

$$3\sqrt{2}=\sqrt{18}\text{ and }\sqrt{18}=3\sqrt{2}$$

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}.

$$3\sqrt{2}=3\sqrt{2}\text{ and }\sqrt{18}=3\sqrt{2}$$

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}.

$$3\sqrt{2}=3\sqrt{2}\text{ and }3\sqrt{2}=3\sqrt{2}$$

Subtract 3\sqrt{2} from both sides.

$$3\sqrt{2}-3\sqrt{2}=0\text{ and }3\sqrt{2}=3\sqrt{2}$$

Combine 3\sqrt{2} and -3\sqrt{2} to get 0.

$$0=0\text{ and }3\sqrt{2}=3\sqrt{2}$$

Compare 0 and 0.

$$\text{true}\text{ and }3\sqrt{2}=3\sqrt{2}$$

Subtract 3\sqrt{2} from both sides.

$$\text{true}\text{ and }3\sqrt{2}-3\sqrt{2}=0$$

Combine 3\sqrt{2} and -3\sqrt{2} to get 0.

$$\text{true}\text{ and }0=0$$

Compare 0 and 0.

$$\text{true}\text{ and }\text{true}$$

The conjunction of \text{true} and \text{true} is \text{true}.

$$\text{true}$$