Unit 1.4  estimating square roots
what do we need to know?
 Perfect square numbers
 Meaning of a square root
 Relationship between perfect squares and square roots
 PERFECT SQUARES have square roots that are WHOLE INTEGERS
 Meaning of a square root
 Relationship between perfect squares and square roots
 PERFECT SQUARES have square roots that are WHOLE INTEGERS
class notes




more information
So far we have only worked with square roots of perfect squares. The square roots of other numbers are not whole numbers.
We might conclude that the square roots of numbers between 4
and 9 will be between 2 and 3, and they will not be whole numbers. Based on the pattern in the table above, we could say that √5 is between 2 and 3. Using inequality symbols, we write: 2<√5<3
It's important to emphasize that ONLY PERFECT SQUARE NUMBERS HAVE SQUARE ROOTS THAT ARE WHOLE NUMBERS. This also means that the numbers that are not perfect squares, the NONPERFECT SQUARES, have square roots that are decimals.
and 9 will be between 2 and 3, and they will not be whole numbers. Based on the pattern in the table above, we could say that √5 is between 2 and 3. Using inequality symbols, we write: 2<√5<3
It's important to emphasize that ONLY PERFECT SQUARE NUMBERS HAVE SQUARE ROOTS THAT ARE WHOLE NUMBERS. This also means that the numbers that are not perfect squares, the NONPERFECT SQUARES, have square roots that are decimals.
HOw can we approximate square roots?
To estimate a square root, follow the following steps:
 Determine the TWO PERFECT SQUARE NUMBERS between which your number is found. The lowest perfect square is called the LOWER SQUARE LIMIT, and te highest perfect square is called the THE UPPER SQUARE LIMIT.
 The square root you are trying to approximate lays between the square roots of the lower and the upper square limits.
 Now determine whether your number is closer to the lower square limit or to the upper square limit:
If your number is EXACTLY halfway between the two squares limits,
the square root's decimal is 0 .5
If your number is closer to the LOWER SQUARE LIMIT,
then your square root has a decimal less than 0.5
If your number is closer to the UPPER SQUARE LIMIT,
then your square root has a decimal higher that 0.5
Remember that this is an approximation, so an educated guess is a good enough answer!
 Determine the TWO PERFECT SQUARE NUMBERS between which your number is found. The lowest perfect square is called the LOWER SQUARE LIMIT, and te highest perfect square is called the THE UPPER SQUARE LIMIT.
 The square root you are trying to approximate lays between the square roots of the lower and the upper square limits.
 Now determine whether your number is closer to the lower square limit or to the upper square limit:
If your number is EXACTLY halfway between the two squares limits,
the square root's decimal is 0 .5
If your number is closer to the LOWER SQUARE LIMIT,
then your square root has a decimal less than 0.5
If your number is closer to the UPPER SQUARE LIMIT,
then your square root has a decimal higher that 0.5
Remember that this is an approximation, so an educated guess is a good enough answer!
In the following examples, I followed the steps detailed above:
the number line method
Look at the following example:
An alternate method  method 2
method 3  using the last digit
here is the solution to the worksheet above (plus another one)
videos that may help
online interactive activities
worksheets





review  workbook
math_8__unit_1.4.pdf  
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