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| Simplifying Square Roots |
Simplifying Square Roots
Let's say you have the radical √363, and you need to simplify it into a both, simplest number, and a number that you can use in specific calculations, where we can do this by trying to find perfect squares within the radical.
So, it's a fact that:
√(x×y) = √x × √y
and this fact allows us to understand that we can seperate the √xy into two separate radicals, √x and √y.
But first, we need to find a factor of 363, that would allow us to pull a perfect square from it. Perfect square numbers include: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144 etc. ,as each of them can become a whole number if these numbers were square rooted.
Now, factors of 363 are: 1, 3, 11, 33, 121 and 363.
If you look, you can see that 121 is among that list, 121×3 is 363, and we can change the radical to show that:
√363 = √(121×3) = √121 × √3
And we can take the square root of 121, where we can turn it into a whole number:
= 11 × √3
Hence, 11√3 is the square root number of 363.
Simplifying Square roots in the Denominator:
Lets' say you have the expression:
2⁄√5
And you wanted to simplify this by removing the radical from the denominator, well you can do this by multiplying this fraction by:
√5⁄√5
Which is equal to one, and you get:
2⁄√5 × √5⁄√5
= 2√5⁄5
because a square root multiplied by itself is the number in the square, the denominator is now a whole number, not a radical anymore. The radical still exists in the top, but this is fine in most cases, as the value itself is still exact.