Problem 47 - College Algebra

Question

Rationalize the denominator. $$\frac{\sqrt{2}}{\sqrt{5}}$$

Step-by-Step Solution

Answer

The rationalized form of the given fraction is \(\frac{\sqrt{10}}{5}\).

Step 1: Identify the denominator to be rationalized.

Here, we have the denominator as \(\sqrt{5}\). This needs to be rationalized.

Step 2: Rationalize the denominator.

To do this, we'll multiply both the numerator and denominator by the same square root term present in the denominator. So, multiply \(\frac{\sqrt{2}}{\sqrt{5}}\) by \(\frac{\sqrt{5}}{\sqrt{5}}\). Remember that \(\frac{\sqrt{5}}{\sqrt{5}}\) is 1, so we're not changing the value of the original fraction, just its appearance.

Step 3: Perform the multiplication.

After the multiplication, the fraction becomes \(\frac{\sqrt{2}*\sqrt{5}}{\sqrt{5}*\sqrt{5}}\). Simplify this to \(\frac{\sqrt{10}}{5}\).