Transcript Mod 7 Square Roots

Roots of Numbers
We are learning to…predict square roots to the
nearest tenth and find the principle root of numbers.
Thursday, June 2, 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 = ____
Because…102 or (10)(10) =100.
What multiplied
by itself is 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 (?)2 = 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…
Difference of 4
20
The perfect square above 20 is…
No whole number times
itself equals 20 but…
Difference of 5
20
The solution must be between 4 and 5…but which is the solution closer to?
4.4
Prediction:__________
(Check with your calculator)
25
5
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…
Difference of 3
84
The perfect square above 84 is…
No whole number times
itself equals 84 but…
Difference of 16
100
10
84
The solution must be between 9 and 10…but which is the solution closer
to?
9.2
Prediction:__________
(Check with 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 positive square
root or “principle square root.”
 If you see opposite symbol outside of a radical you are finding the negative
square root.