How to simplify square root of 50?
Understand the Problem
The question is asking how to simplify the mathematical expression of the square root of 50. This involves finding the prime factorization of 50 and identifying any perfect squares that can be factored out of the square root.
Answer
$5\sqrt{2}$
Answer for screen readers
The simplified form of the square root of 50 is $5\sqrt{2}$.
Steps to Solve
- Find the prime factorization of 50
We start by breaking down 50 into its prime factors. $$ 50 = 2 \times 25 $$ Next, notice that 25 can be factored into: $$ 25 = 5 \times 5 $$ So, the complete prime factorization of 50 is: $$ 50 = 2 \times 5^2 $$
- Identify perfect squares
In our prime factorization, $5^2$ is a perfect square. We can take the square root of that out of the square root.
- Rewrite the square root expression
Using the properties of square roots, we can separate the perfect square from the rest: $$ \sqrt{50} = \sqrt{2 \times 5^2} $$
- Simplify the expression
Taking the square root of the perfect square $5^2$ gives us 5: $$ \sqrt{50} = \sqrt{2} \times \sqrt{5^2} = 5\sqrt{2} $$
The simplified form of the square root of 50 is $5\sqrt{2}$.
More Information
The square root of 50 can be simplified because it contains a perfect square factor. Knowing how to break down numbers into their prime factors is useful in simplifying square roots and other mathematical expressions.
Tips
- Forgetting to include the perfect square when simplifying: Always check for perfect squares in the factorization.
- Miscalculating the prime factors: Ensure the factors are prime and calculated correctly.
