Solve sqrt{20}=sqrt{80}*1/2

$$\sqrt{ 20 } = \sqrt{ 80 } \times \frac{ 1 }{ 2 }$$

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}.

$$2\sqrt{5}=\sqrt{80}\times \frac{1}{2}$$

Factor 80=4^{2}\times 5. Rewrite the square root of the product \sqrt{4^{2}\times 5} as the product of square roots \sqrt{4^{2}}\sqrt{5}. Take the square root of 4^{2}.

$$2\sqrt{5}=4\sqrt{5}\times \frac{1}{2}$$

Multiply 4 and \frac{1}{2} to get \frac{4}{2}.

$$2\sqrt{5}=\frac{4}{2}\sqrt{5}$$

Divide 4 by 2 to get 2.

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

Subtract 2\sqrt{5} from both sides.

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

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

$$0=0$$

Compare 0 and 0.

$$\text{true}$$