Question

Simplify the expression. $$\sqrt{2} \cdot \sqrt{8}$$

Short answer

The simplified result of the expression is 4

Step-by-step solution

Express the given expression

The given expression is \( \sqrt{2} \cdot \sqrt{8} \).

Simplify square root of 8

The square root of 8 can be reduced by breaking 8 down into \(2^3\). So, \( \sqrt{8} = \sqrt{2^3} = 2\sqrt{2}\), because the square root of \(2^2\) is 2.

Apply the simplified square root

Substitute \(2\sqrt{2}\) for \(\sqrt{8}\) to get \( \sqrt{2} \cdot 2\sqrt{2} \).

Simplify the expression

The square root of 2 times the square root of 2 is 2. As such, the expression can be simplified further into \(2 \cdot 2 = 4\).