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Square roots

The square root of a number is the factor that we can multiply by itself to get that number.
The symbol for square root is \sqrt{ } .
Finding the square root of a number is the opposite of squaring a number.
4×4\blueD4 \times \blueD4 or 42\blueD4^2 =16= \greenD{16}
So 16=4\sqrt{\greenD{16}} = \blueD4
If the square root is a whole number, it is called a perfect square! In this example, 16\greenD{16} is a perfect square because its square root is a whole number.
Want to learn more about finding square roots? Check out this video.

Finding square roots

If we can't figure out what factor multiplied by itself will result in the given number, we can make a factor tree.
36=?\Large{\sqrt{36} = \text{?}}
Here is the factor tree for 3636:
So the prime factorization of 3636 is 2×2×3×32\times 2\times 3\times 3.
We zoeken 36\sqrt{36}, dus willen we de priemfactoren in twee identieke groepjes verdelen.
Notice that we can rearrange the factors like so:
36=2×2×3×3=(2×3)×(2×3)36 = 2 \times 2 \times 3 \times 3 = \left(2\times 3\right) \times \left(2 \times 3\right)
Dus (2×3)2=62=36\left(2\times 3\right)^2 = 6^2 = 36.
So, 36\sqrt{36} is 6 6.


Want to try more problems like this? Check out this exercise: Finding square roots
Or this challenge exercise: Equations with square and cube roots