Simplify square root of 20.
Understand the Problem
The question is asking for the simplification of the square root of 20. To solve this, we will factor 20 into its prime factors and identify perfect squares to simplify the expression.
Answer
2\sqrt{5}
Answer for screen readers
The square root of 20 simplifies to 2√5
Steps to Solve
- Factorize 20 into prime factors
First, identify the prime factors of 20: $$ 20 = 2^2 imes 5 $$
- Rewrite the square root expression
Use the prime factors to rewrite the square root of 20: $$ \sqrt{20} = \sqrt{2^2 imes 5} $$
- Simplify the square root
Separate the square root into two parts and simplify: $$ \sqrt{2^2 imes 5} = \sqrt{2^2} \times \sqrt{5} = 2 \times \sqrt{5} $$
The square root of 20 simplifies to 2√5
More Information
Simplifying the square root of 20 allows to see it in a more reduced form, which might be useful in various mathematical contexts.
Tips
A common mistake is forgetting to pull out the entire perfect square from under the root, resulting in an incorrect simplification.
