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.
Answer
Approximately 4.89898 or exactly 2\sqrt{6}
Answer for screen readers
The square root of 24 is approximately 4.89898 or exactly 2\sqrt{6}.
Steps to Solve
- 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.
- 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:
$$\sqrt{24} = \sqrt{4 \times 6} = \sqrt{4} \times \sqrt{6} = 2\sqrt{6}$$
- 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}.
More Information
Square roots of non-perfect squares are irrational numbers and can be approximated using decimal values, or expressed in simplest radical form.
Tips
Common mistakes include not reducing the square root to its simplest radical form or incorrectly estimating the decimal value of the square root.
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