Simplify sqrt 250 j^4 o^5
Everything is under the radical.
√250j^4o^5
factor out perfect squares
√25√10√j^4√o^4√o
now extract the square roots of the squares
5j^2o^2√10o
Now you know whey o is seldom used as a variable name...
That was actually the first time I saw o as a variable...
Never mind, the square root.
To simplify the expression √250j^4o^5, we need to first break down the numbers and variables inside the square root.
Let's start by factoring out all perfect square factors from the number under the square root. In this case, we see that 250 can be factored into 25 * 10. The perfect square factor is 25, so we can rewrite the expression as:
√(25 * 10)j^4o^5
Now, let's simplify the square root of 25. Since 25 is a perfect square, its square root is just the number itself. Therefore, we can simplify further:
5√(10)j^4o^5
Next, we simplify the variable terms. j^4 is equivalent to (j^2)^2, and since j^2 is the square of j, we know that √(j^2) = j. Applying this logic, we have:
5√(10)j^4o^5 = 5√(10)j^2j^2o^5
Since we now have j^2 in front of the square root, we can take it out and simplify further:
5j^2√(10)jo^5
Finally, we can rearrange the terms to put the variables together:
5j^2jo^5√(10)
So, the simplified form of √250j^4o^5 is 5j^2jo^5√(10).