Transcript Roots of Numbers - Solon City Schools

Roots of Numbers
We are learning to…predict square roots to the nearest
tenth and find the principle root of numbers.
Sunday, March 27, 2016
Fill in your name, date, period, and learning target…then try the
warm up questions and put your pencil down!
Roots of Numbers

Square Root – A number when multiplied by
itself (squared) produces the given number.


The opposite or inverse of using an exponent of 2.
The symbol to indicate finding a square root
is called a “radical symbol.”
 It looks like:
#

Your job is to think of the number that when multiplied by
itself equals the number inside the radical symbol.
Examples:
16
4 Because…42 or (4)(4) =16.
= ____
What multiplied
by itself is 16?
10
100 = ____
What multiplied
by itself is 100?
Because…102 or (10)(10) =100.
Examples:
12
144 = ____
Because…122 or (12)(12) =144.
What multiplied
by itself is 144?
20
400 = ____
What multiplied
by itself is 400?
Because…202 or (20)(20) =400.
Examples:
15
225 = ____
Because…152 or (15)(15) =225.
What multiplied
by itself is 225?
10, 000 = 100
____
What multiplied by
itself is 10,000?
Because…1002 or (100)(100) =10,000.
Reflection

Josh believes that 16  8 . What did Josh do
wrong? Help him to correct his error.



Remember that 16  8 does not mean 16 ÷ 2.
It means…what number times itself equals or
(?)(?) = 16?
The correct solution is 16  4
Predicting square roots of non-perfect
squares.
Sometimes you will have to find the square root of a number that is not a
perfect square…this means that you solution will not be a whole number.
For example:
16
4
The perfect square below 20 is…
The perfect square above 20 is…
Difference of 4
Difference of 5
No whole number times
itself equals 20 but…
20
25
20
5
The solution must be between 4 and 5…but which is the solution closer to?
Prediction:__________
(Check with your calculator)
Predicting square roots of non-perfect
squares.
Sometimes you will have to find the square root of a number that is not a
perfect square…this means that you solution will not be a whole number.
For example:
81
9
The perfect square below 84 is…
The perfect square above 84 is…
Difference of 3
Difference of 16
No whole number times
itself equals 84 but…
84
100
84
10
The solution must be between 9 and 10…but which is the solution closer to?
Prediction:__________
(Check with your calculator)
Predicting square roots of non-perfect
squares.

Predict the square root of 12 with your group.

When you are done check the prediction on your
calculator.
Negative Roots of Numbers



For every square root there are actually 2 solutions. This because...
 (Negative Number) (Negative Number) = A Positive Number

For Example:
 (5)(5) = 25 and also (-5)(-5) = 25
 So… 25  5 or  5
When you see the “radical symbol” just assume you are taking the
“principle square root.”
(POSTIVE SQUARE ROOT)
If you see negative outside of a radical you are finding the NEGATIVE
SQUARE ROOT.
Extension:

What do you think 3 8 means? What is the
solution?
 3 8 is asking you to find ?3=8 or (?)(?)(?) = 8.
3
 Since (2)(2)(2) = 8, 8  2