# What is the square root of 24?

#### Understand the Problem

The question is asking for the square root of the number 24, which involves determining what number multiplied by itself equals 24.

Approximately 4.89898 or exactly 2\sqrt{6}

The square root of 24 is approximately 4.89898 or exactly 2\sqrt{6}.

#### Steps to Solve

1. Identify that 24 is not a perfect square

Realize that there is no integer that, when squared, equals 24. This means the answer will be an irrational number, which might involve approximation if a decimal answer is needed.

1. Express the square root in simplest radical form

Expras $\sqrt{24}$ in terms of simpler square roots. To do this, factor 24 into its prime components and simplify as follows:

$$\sqrt{24} = \sqrt{4 \times 6} = \sqrt{4} \times \sqrt{6} = 2\sqrt{6}$$

1. Approximate the square root

Use a calculator to find a decimal approximation for $\sqrt{6}$. We know that $\sqrt{4}$ is 2 and $\sqrt{9}$ is 3, so $\sqrt{6}$ falls between these two values. Using a calculator, we find:

$$\sqrt{6} \approx 2.44949$$

Thus, the approximation for $\sqrt{24}$ is:

$$2 \times 2.44949 \approx 4.89898$$

The square root of 24 is approximately 4.89898 or exactly 2\sqrt{6}.