How to Simplifying Square Roots ?

To simplify square roots,

1. Factor the radicand into primes.
2. Circle each pair of like numbers.
3. For each pair of like numbers, place the individual number outside the radical sign and erase the pair inside the radical. The number outside is called the coefficient.
4. Multiply the numbers outside the radical sign.
5. Multiply the numbers inside the radical sign.

Example 1: Simplify √30.
√30 = √5.6 = √2.3.5 = √30
30 has no pairs of factors, so √30 is in simplest form.

Example 2: Simplify √125.
√45 = √5.9 = √3.3.5 = √(3.3).5 = 3√5
The prime factorization of 45 is . Since there's one pair of 3's, place a 3 outside of the radical sign and erase the pair of 3's inside the sign.

Example 3: Simplify √36
√36 = √6.6 = 6
36 wasn't factored into primes, because it's easy to notice that the number is a perfect square. Using the original method gives the same answer.

√36 = √6.6 = √2.3.2.3 = √(2.2).(3.3)
Try these on your own:

Example 4: Simplify √48
Example 5: Simplify √300.