Square root of 50 in simplest radical form
Understand the Problem
The question is asking to simplify the square root of 50 into its simplest radical form, which involves breaking down the number under the square root into its prime factors and identifying perfect squares.
Answer
$5\sqrt{2}$
Answer for screen readers
The simplified form of the square root of 50 is $5\sqrt{2}$.
Steps to Solve
- Identify the prime factors of 50
To simplify the square root of 50, we first find its prime factors. The number 50 can be factored as:
$$ 50 = 2 \times 25 $$
Next, recognize that 25 is a perfect square:
$$ 25 = 5^2 $$
So, we have:
$$ 50 = 2 \times 5^2 $$
- Apply the product property of square roots
Now that we have the prime factorization, we can use the product property of square roots, which states that:
$$ \sqrt{a \times b} = \sqrt{a} \times \sqrt{b} $$
We can apply this to our expression:
$$ \sqrt{50} = \sqrt{2 \times 5^2} = \sqrt{2} \times \sqrt{5^2} $$
- Simplify the expression
Since the square root of $5^2$ is $5$, we can simplify further:
$$ \sqrt{50} = \sqrt{2} \times 5 = 5\sqrt{2} $$
Thus, we have simplified the square root of 50.
The simplified form of the square root of 50 is $5\sqrt{2}$.
More Information
The square root of a number can often be simplified by breaking it down into its prime factors, allowing for the extraction of perfect squares. In this case, the perfect square was 25, which made the simplification straightforward.
Tips
- Forgetting to factor out all perfect squares can lead to an unsimplified answer.
- Confusing the square root of a product with the product of square roots without properly identifying perfect squares.