Question

Simplify the expression. $$\sqrt{5} \cdot \sqrt{8}$$

Short answer

The simplified expression of \( \sqrt{5} \cdot \sqrt{8} \) is 2\( \sqrt{10} \)

Step-by-step solution

Identify multiplication of square roots

Here we see that the exercise involves the multiplication \( \sqrt{5} \cdot \sqrt{8} \). According to the properties of square roots, multiplication inside the radical can be written as \( \sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b} \). We apply this property to our problem.

Apply the root multiplication property

By the property of multiplication inside the radical, the expression \( \sqrt{5} \cdot \sqrt{8} \) simplifies to \( \sqrt{5 \cdot 8} \), which equals \( \sqrt{40} \).

Simplify the square root

Now, we need to simplify the \( \sqrt{40} \). The number 40 can be broken down into its factors as 4 times 10. Thus, \( \sqrt{40} \) is equivalent to \( \sqrt{4 \cdot 10} \). Let's simplify that.

Use the root multiplication property

Using the definition of square root multiplication, \( \sqrt{4 \cdot 10} \) equals \( \sqrt{4} \cdot \sqrt{10} \), which is simple to determine as 2 and \( \sqrt{10} \).

Express the final answer

The final step is to express our answer. The multiplication of \( \sqrt{5} \cdot \sqrt{8} \) simplifies to 2\( \sqrt{10} \) as the final result.