**If a square root is NOT a Perfect Square it is an IRRATIONAL Number.
We can estimate the values of these square roots WITHOUT using a calculator:
To solve this, you just need to find the two perfect squares that are directly above and below the number.
Let's Break Down Example 1:
STEP ONE: Identify the non perfect square.
This will be given to you in the problem. The non perfect square in this example is √8
STEP TWO: Identify the perfect squares that the non perfect square falls between.
Use your knowledge of perfect squares to determine that the perfect squares the √8 falls between is √4 and √9
You can create a number line to help you visualize this:
This will be given to you in the problem. The non perfect square in this example is √8
STEP TWO: Identify the perfect squares that the non perfect square falls between.
Use your knowledge of perfect squares to determine that the perfect squares the √8 falls between is √4 and √9
You can create a number line to help you visualize this:
STEP THREE: Take the square root the perfect squares
√4= 2 and √9=3, Therefore, I know that the √8 falls between the integers 2 and 3.
STEP FOUR: Estimate the non perfect square.
I know that √8 cannot be smaller √4 or bigger than √9
Also, I know that √8 is closer to the √9 than the √4.
Therefore, I would estimate that the √8 is 2.8
√4= 2 and √9=3, Therefore, I know that the √8 falls between the integers 2 and 3.
STEP FOUR: Estimate the non perfect square.
I know that √8 cannot be smaller √4 or bigger than √9
Also, I know that √8 is closer to the √9 than the √4.
Therefore, I would estimate that the √8 is 2.8
*Hint* The Decimal MATTERS!
Look at the distance between the perfect squares and the non perfect square to see where the number falls. Don't just guess, use logic!