Download Finding Square Roots (Exact and Approximate) Method #1 – Prime

Finding Square Roots
(Exact and Approximate)
Method #1 – Prime Factorization
1) Create a factor tree for the number.
2) Factor the number until only prime factors are on the bottom
row of the tree.
3) Collect all factors into two identical groups.
4) Multiply the numbers in one of the groups – this will give you
your answer.
Method #2 – Approximating a Square Root Using Perfect Squares
1) Find the perfect square smaller than your number.
2) Find the square root of this perfect square. This square root
will be the whole number part of your answer.
3) Find the perfect square larger than your number. Find the
square root of this number.
4) Compare your original number with the two perfect squares.
Which one is it closer to? Is it in the middle? Decide which
decimal best describes how close your number is to the
perfect squares.
Method #3 – Cutting Up Squares Method
1) Find the perfect square closest to your number, but smaller.
2) Draw a square and divide it into the number of squares in
the perfect square.
3) Draw the extra squares you have.
4) Cut up the extra squares you have into enough pieces that
they will evenly fit around two of the edges of the perfect
square you drew.
5) Count the squares (including the part squares) along one
edge. This is your square root.
Example of Prime Factorization
1)
36
12
x
2)
36
3
12
4
2
3) (2 x 3) (2 x 3)
x
x
2
x
x
3
3
3
x
x
4) 2 x 3 = 6, √36 = 6
3
3
Example of Approximating
1) √30,
25
2) √25 = 5,
5.
3) 36, √36 = 6
4) 30 is in the middle of 25 and 36, in the middle = 0.5
√30 = 5.5
 If the number is one more than the smaller perfect
square, use the decimal 0.1
 If the number is one less than the larger perfect square,
use the decimal 0.9
 If the number is in the middle of both perfect squares,
use the decimal 0.5
 If the number is closer to the smaller perfect square,
use the decimals 0.2 or 0.3 or 0.4
 If the number is closer to the larger perfect square, use
the decimals 0.6 or 0.7 or 0.8