Question

Evaluate the expression. Give the exact value if possible. Otherwise, approximate to the nearest hundredth. $$\sqrt{0.04}$$

Short answer

The principal square root of 0.04 is 0.2.

Step-by-step solution

Understanding the notion of square root

The square root of a number x is defined as a value that, when multiplied by itself, gives the original number x. For any number, there are two square roots – one positive and one negative. However, when we calculate the square root, we are usually interested in the principal square root, which is the positive one.

Calculating the square root

To find the square root of 0.04, think about which number, when multiplied by itself, will give you 0.04. You can, for convenience, recall that 0.04 is the same as \( \frac{4}{100} \), or \( 0.2 \times 0.2 \). Therefore, \( \sqrt{0.04} \) is 0.2.