Find the square root of 250.
O 25sqrt(10)
O 250
O 5sqrt(10)
O 10sqrt(5)
The square root of 250 is 5√10
To find the square root of 250, we can simplify it by factoring out perfect squares.
First, let's identify any perfect square factors of 250. The only perfect square factor is 25 (5 * 5).
Now, we can rewrite 250 as a product of perfect squares:
250 = 25 * 10
Taking the square root of both sides, we have:
√250 = √(25 * 10)
Using the property of square roots that states √(a * b) = √a * √b, we can split the square root of the product into the product of the square roots:
√(25 * 10) = √25 * √10
Simplifying further, √25 is equal to 5:
√(25 * 10) = 5 * √10
Therefore, the square root of 250 is 5√10.
So the correct choice is O 5sqrt(10).
To find the square root of 250, you can either use a calculator or simplify the number manually.
Using a calculator:
1. Enter the number 250 into the calculator.
2. Press the square root (√) button.
3. The calculator will give you the square root of 250 as approximately 15.8113883008.
Manually simplifying the number:
1. Start by breaking down 250 into its prime factors: 2 * 5 * 5 * 5.
2. Group the pairs of identical prime factors: 2 * (5 * 5) * 5.
3. Take one factor from each pair and move it outside the square root: 5 * √(2 * 5).
4. Simplify the numbers outside the square root: 5√(10).
Therefore, the square root of 250 simplifies to 5√10, which is option O: 5sqrt(10).