What is √125 simplified?
√125 simplified is 5√5.
To simplify √125, we can break it down into its prime factors.
First, we notice that 125 can be divided evenly by 5, so we have 125 = 5 * 25.
Next, we continue breaking down 25 into its prime factors. We see that 25 can be divided evenly by 5, so we have 25 = 5 * 5.
Therefore, we can simplify √125 as √(5 * 5 * 5).
Taking out one factor of 5 from the square root, we get 5√5.
So, √125 simplifies to 5√5.
To simplify the square root of 125, we need to find the largest perfect square that is a factor of 125.
First, let's find the prime factors of 125:
125 = 5 * 5 * 5 = 5^3
We can see that 5^2 is a perfect square that is a factor of 125.
Now, we can rewrite 125 as the product of 5^2 and another number:
125 = 5^2 * 5 = 25 * 5
Therefore, we can simplify the square root of 125 as follows:
√125 = √(25 * 5)
Using the property of square roots, we can split the square root of a product into the product of individual square roots:
√(25 * 5) = √25 * √5
Since the square root of 25 is a perfect square (5), we can simplify further:
√25 * √5 = 5 * √5
Therefore, the simplified form of √125 is 5√5.