SOLUTION: What is the formula for finding the square root of 225? I know the answer is 15, I'm trying to figure out the formula, please. I know how to figure it using the factor tree, but I

Question 568138: What is the formula for finding the square root of 225? I know the answer is 15, I'm trying to figure out the formula, please. I know how to figure it using the factor tree, but I don't know how to do the square root formula Thank You so much!
P.S.
When I clicked on the drop down list to pick a topic, nothing came up. There were no words, just blank space & a check mark, so I'm sorry if the topic was off.

Found 2 solutions by richard1234, homeworkhedgehog:
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
There's not much of a formula. Square root is defined as "what number times itself equals the given number." Since 15*15 = 225, the square root of 225 is 15.
Answer by homeworkhedgehog(9) (Show Source): You can put this solution on YOUR website!
The way to simplify square roots involves finding their factors and grouping.
The way I like to explain this is that you need to find all the prime factors of the number you want to take the root of, circle (on paper) all the pairs of numbers that you have. Now, each of these pairs can be "pulled out" of the square root. But when they do get pulled through this square root, the root acts as a kind of filter that allows only one "spokesman" for each group. For example, if I have

then factored out that is the same as
.
There is only one complete pair of 2's here that would get pulled out. The one leftover 2 will remain inside the root. We have to obey the spokesman rule for our pair of 2's, so only one 2 gets to represent the pair on the outside of the root. Therefore,

would be the simplified answer where the two 2's in parentheses are the pair of 2's that I am pulling out.
The same goes for 225, except we just don't have anything leftover or remaining on the inside except a factor of 1. That is why your answer is just a solid integer, 15.

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Of course, you could just pull out the pair of 15's, but this is the drawn out way you can solve any square root by.
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