Name: _________________________________ Math 8

2.7: Find Square Roots and Compare Real Numbers

Goals: *Find square roots of numbers *Approximate a square root between two integers *Order real numbers *Evaluate cube roots *Classify real numbers

__________________________________________________________________________________________

SQUARE ROOTS: One of two _______________ factors of a number. (The number times ___________). Ex: = _____ because:√9 Ex: = _______ because:√36

PERFECT SQUARES : a number who’s _____________ ___________ is an _____________. 1, ______, ______, ______, ______, ______, ______, ______, ______, ______, ______, ______, ______, ______, ______, ...

Evaluate the given expression:

Ex: √16 Ex: √64 Ex: √81

Ex: √100 Ex: √121 Ex: √49 Ex: Think about the number 4. What number times itself will have an answer of 4? _______ Is there any other number you can think of that would also have an answer of 4 when multiplied by itself?

Mrs Kearney

equal itself3 3.3193 6 6.6360

square root integer

4 9 16 25 36 49 64 81 100 121 144 169

196 225

2

2 2 240

Name: _________________________________ Math 8

All numbers have two square roots, one is ___________________ and one is ____________________.

Pay attention to notation to know which one you are being asked for.

Ex: − √9 Ex: ± √64 Ex: √25

Ex: ± √100 Ex: − √81 Ex: √144

Solve: 6x2 = 3 In this case, you are being asked to provide all possible values for x, that when you square it, would equal 36. What are these numbers?

Solve:

Ex: x2 = 1 Ex: 9x2 = 4 Ex: 4x2 = 6

QUESTION: How can you prove something is a square root? PONDER: What do you think the is?√810000 PROVE: Prove your answer either is or isn’t correct by using your logic from QUESTION.

Positive negative

120

band 6

rr rr rrX x X

multiplyitbyitself

900

900900000000

8100TOV

Name: _________________________________ Math 8

Now let’s find the square root of the following examples:

Ex: √400 Ex: √160, 000 Ex: √4900

Can you create an example similar to ones above?

QUESTION: How can you prove something is a square root? PONDER: What do you think the is?√0.0121 PROVE: Prove your answer either is or isn’t correct by using your logic from QUESTION.

Now let’s find the square root of the following examples:

Ex: √0.0081 Ex: √0.0064 Ex: √0.000144

810000

200 4000

56000000

60000

0.011

0.0110.011

0.000121

0.090 0.080 0.0120

Name: _________________________________ Math 8

Estimate Square Roots: Ex: √40

1. Find the two closest _____________ __________. One above and one below.

2. Put the numbers in order from ___________ to ____________.

3. Find the ______________ _________ of the two _____________ _______________.

4. Pick the _______________ one. Ex: √110 Ex: √20

Ex: √38 Ex: √8

Evaluate the expression.

Ex: when x = 8111 − √x Ex: when x = 1006√x + 3

Ex: when x = 646− 3√x + 3 Ex: when x = 3645 − 8 · √x

perfect savares536540Fea6 Fo't

least greatest

savate rook perfect squares

closest

Foo Fu 16T VEDO It 04 5

56 49T yr r97 2 30

H ti 6 311 9 6.10 3

6013630

3 136 54 8Bb38136 54 8624136 54 48O O

Name: _________________________________ Math 8

Cube Roots:

If means to find the square root (the number times itself) that equals x, what do you think means? √x √3 x Evaluate:

Ex: √3 8 Ex: √3 27 Ex: √3 64

IRRATIONAL NUMBER: numbers that cannot be written as __________________. This includes Pi, decimals that do not _____________ or __________________, which is all square roots of non-perfect squares.

Classify the following numbers using all names that apply:

Number Whole Integer Rational Irrational

√24

√100

− √81

− √25

√30

21

cuberoot the timesitself3times

fractions

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