Solve sqrt{8}*sqrt{2}=sqrt{2*2}=sqrt{16}

$$\sqrt { 8 } \cdot \sqrt { 2 } = \sqrt { 2 \cdot 2 } = \sqrt { 16 }$$

Verify

Solution Steps

Factor 8=2\times 4. Rewrite the square root of the product \sqrt{2\times 4} as the product of square roots \sqrt{2}\sqrt{4}.

$$\sqrt{2}\sqrt{4}\sqrt{2}=\sqrt{2\times 2}\text{ and }\sqrt{2\times 2}=\sqrt{16}$$

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

$$2\sqrt{4}=\sqrt{2\times 2}\text{ and }\sqrt{2\times 2}=\sqrt{16}$$

Calculate the square root of 4 and get 2.

$$2\times 2=\sqrt{2\times 2}\text{ and }\sqrt{2\times 2}=\sqrt{16}$$

Multiply 2 and 2 to get 4.

$$4=\sqrt{2\times 2}\text{ and }\sqrt{2\times 2}=\sqrt{16}$$

Multiply 2 and 2 to get 4.

$$4=\sqrt{4}\text{ and }\sqrt{2\times 2}=\sqrt{16}$$

Calculate the square root of 4 and get 2.

$$4=2\text{ and }\sqrt{2\times 2}=\sqrt{16}$$

Compare 4 and 2.

$$\text{false}\text{ and }\sqrt{2\times 2}=\sqrt{16}$$

Multiply 2 and 2 to get 4.

$$\text{false}\text{ and }\sqrt{4}=\sqrt{16}$$

Calculate the square root of 4 and get 2.

$$\text{false}\text{ and }2=\sqrt{16}$$

Calculate the square root of 16 and get 4.

$$\text{false}\text{ and }2=4$$

Compare 2 and 4.

$$\text{false}\text{ and }\text{false}$$

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

$$\text{false}$$