Solve sqrt{20}=sqrt{4}*sqrt{5}=2sqrt{5}

$$\sqrt { 20 } = \sqrt { 4 } \cdot \sqrt { 5 } = 2 \sqrt { 5 }$$

Verify

Solution Steps

Factor 20=2^{2}\times 5. Rewrite the square root of the product \sqrt{2^{2}\times 5} as the product of square roots \sqrt{2^{2}}\sqrt{5}. Take the square root of 2^{2}.

$$2\sqrt{5}=\sqrt{4}\sqrt{5}\text{ and }\sqrt{4}\sqrt{5}=2\sqrt{5}$$

Calculate the square root of 4 and get 2.

$$2\sqrt{5}=2\sqrt{5}\text{ and }\sqrt{4}\sqrt{5}=2\sqrt{5}$$

Calculate the square root of 4 and get 2.

$$2\sqrt{5}=2\sqrt{5}\text{ and }2\sqrt{5}=2\sqrt{5}$$

Subtract 2\sqrt{5} from both sides.

$$2\sqrt{5}-2\sqrt{5}=0\text{ and }2\sqrt{5}=2\sqrt{5}$$

Combine 2\sqrt{5} and -2\sqrt{5} to get 0.

$$0=0\text{ and }2\sqrt{5}=2\sqrt{5}$$

Compare 0 and 0.

$$\text{true}\text{ and }2\sqrt{5}=2\sqrt{5}$$

Subtract 2\sqrt{5} from both sides.

$$\text{true}\text{ and }2\sqrt{5}-2\sqrt{5}=0$$

Combine 2\sqrt{5} and -2\sqrt{5} 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}.

$$\text{true}$$