What is the square root of 20 simplified?
Understand the Problem
The question is asking for the simplified form of the square root of 20. To solve it, we can break it down into its prime factors and simplify.
Answer
$2\sqrt{5}$
Answer for screen readers
The simplified form of the square root of 20 is $2\sqrt{5}$.
Steps to Solve
- Factor the number under the square root
We start with the number 20. First, we factor it into its prime components: $$ 20 = 2 \times 10 $$ Next, we can factor 10 further: $$ 10 = 2 \times 5 $$ So, we can express 20 as: $$ 20 = 2^2 \times 5 $$
- Identify perfect squares
In the factors of 20, we see that $2^2$ is a perfect square. This is important for simplifying the square root.
- Apply the square root to each factor
Now we apply the square root to the factored form of 20: $$ \sqrt{20} = \sqrt{2^2 \times 5} $$
- Separate the square root of the perfect square
We can separate the square root of the perfect square from the other factor: $$ \sqrt{20} = \sqrt{2^2} \times \sqrt{5} $$
- Simplify the expression
Since the square root of $2^2$ is 2, we can simplify further: $$ \sqrt{20} = 2 \sqrt{5} $$
The simplified form of the square root of 20 is $2\sqrt{5}$.
More Information
The square root of 20 simplifies to $2\sqrt{5}$, which is considered a simpler and more useful form, especially in problems needing exact values rather than decimal approximations. This can help in further calculations and in understanding relationships in geometry and algebra.
Tips
- Not recognizing that $2^2$ is a perfect square and leaving the square root as $\sqrt{20}$.
- Forgetting to simplify the square root of each factor correctly.
