The square root of a number is the opposite of squaring a number.
To find a square root of a number means finding one number that multiplies itself.
The symbol for a square root is
. It is called a radical sign.
For example: 
because 5
is 25 and 12 is 144.
These are called “Perfect Squares” because the solutions are whole numbers.
There are square root equations that aren’t so perfect.
An example is 
.
The square root of 20 would not be a whole number, and instead would be a decimal which makes things complicated. You can instead simplify it.
Remember that you can separate
square roots without changing its value. 5 x 4 = 20. In this case, 
x 
= . Since = 2, it then becomes 2 because the 5 can no longer be simplified.
For Example: 
= x 
= 2 → Since does not become a
whole number, we separate into a perfect square multiplied by another. The
“2”
goes out of the root and “6” stays in because it cannot be simplified.
= 
x 
= 3 → 9
is the greatest “perfect square” that multiplies with another number to become
90. A “3” goes out and the “10”
stays inside because it can’t be simplified.
The same rules apply when you are multiplying square roots
of fractions, but you can’t have a square root number as a denominator. So in
order to get rid of it, you must “rationalize
the denominator.”
Remember that any number divided by itself equals to 1 and it also applies to square roots. In order to rationalize the denominator, you multiply the square rooted fraction by the denominator over itself.
For Example: 
x 
= 
= 
→ When
multiplying square root of fractions, the same rules apply as before, but the
denominator can’t be a square
root, so you multiply the fraction by “1”, or the denominator over itself. From there, you simplify just like before.
= 
→ In
this case, you do not need to multiply by “1” because the denominator can
already be simplified without doing
so. The numerator doesn’t matter if it has a square root.
Now You Try:
Simplify the expressions.
1. 2. 
3. 
4. 
5. 
6. 
7. 
8. 
9. 
10. 
11. 
12. 
