2 3- rational irrational square roots approximating.notebook · 2019. 3. 27. · 2_3...

2_3 Rational_Irrational Square Roots_Approximating.notebook

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M4- 1.2 Rational & Irrational Square Roots & Approximations

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Examples: Notes:

EQ: How are rational numbers different from other number sets?

Square: a number multiplied by itself• 3 x 3 = 32 = 9• 3 squared

Radical Sign: • Symbol for square root

Square Root: Inverse operation to a square

Finding which number that is multiplied by itself to create the number• Finding the factor that was used 2 times.• √9 = 3 because 2 x 3 =9Perfect Square: square of a whole number• 49 = 72 and 7 is a whole number, an integer &

rational.


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Examples: Notes:


Non- Perfect Squares:• Irrational number that lies between 2

integers.• We can approximate its value to a decimal to

know how far between those two integers it falls.

• 20 = irrational because 20 isn't a perfect square.

• It will end up being a number somewhere between 4 & 5.


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Examples: Notes:


Approximating non-perfect square- the decimal way: √201. Find the two perfect squares a number

lies between?> 16 and 25> √25 = 5> √16 = 4 so the square root of 20 must be

a little more than 4.2. Find the "little more"

> Is the "non-perfect square" 20 closer to 16 or 25?

> It seems to be right in the middle. > Pick a number in between 4 & 5.

3. Multiply that number by itself.> 4.4 x 4.4 = 19.36> 20 - 19.36 = 0.64

4. Can you get closer to 20?> Try 4.5 x 4.5 = 20.25> 20 - 20.25 = -0.25> 4.5 is the BEST estimate for the square

root of 20.


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Examples: Notes:


Approximating non-perfect square- the fraction way: 1. Find the two perfect squares a number lies

between?> 16 < 20 < 25

2. What 2 integers will the square root lie between?

> √25 = 5> √16 = 4 > 4 < ___ < 5

3. Figure out which perfect square your number is closest to.

> The square root of that number becomes your whole number.

> 20 is closer to 16... So 4 is your whole number. 4. Find the "little more" fraction style

> Set up a mixed number> Numerator = the number MINUS smaller

perfect square> Denominator = bigger perfect square MINUS the

smaller perfect square.> Change to a decimal.

20 is closer to 16, than 25. SO: √16 = 4

= 4.44


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Examples: Notes:


Calculating Non- Perfect Square Root: Staudohar's Way (Factor Trees)1. Make a tree of factors.2. If a number is a square, write only one

factor.> Since √4 = 2, the 2 is taken out & placed

on the outside of the radial sign.> Whatever factors do not make a perfect

square, are left on the inside of the radical sign. – If more than one factor is either

outside or inside, multiply them together.

> The answer to the √20 = 2√5

4 5

2

x 2 = 4.472135954999579


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Examples: Notes:


Calculating Square Root of a Fraction of perfect squares: 1. Find the square root of the numerator.2. Find the square root of the denominator.3. Write as a fraction.4. Calculate the decimal.

= 410

= 0.40


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Examples: Notes:


Calculating Square Root of a Fraction (non-perfect squares): 1. Write as separate square roots: as

numerator & denominator.2. To clear out the square root from the

denominator, multiply both the numerator & denominator by the denominator.

> The square root x square root = that number.

3. Multiply the numerators together to get a new number inside the radical.

4. Using any method, find the square root of the numerator.

5. Simplify fraction by cross canceling.> You can only cancel what is on the outside

of the radical sign. 6. Divide the numerator by the denominator

to get the answer.

=√7√20 √20

√20 =

√7 √2020 =

√14020

140

7 20

4 5

2

2√3520

=

35 - 25 = 1036 - 25 = 11

= 0.91

5.9110

√3510

=

√35 = (5__6) (25__36)closest to 6, but < 6

= 0.59


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Homework: Rational & Irrational Square Root Worksheet


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Whiteboard Race

Find the square root of a number using either the decimal way, fraction way or factor tree way. Circle your answer.


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Homework‐ Online

“Approximating Irrational Square Roots” wkst

“Finding Rational & Irrational Square Roots” Worksheet


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Approximating Irrational Square Roots


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Key“Finding Rational & Irrational Square Roots” Worksheet

1² 2² 3² 4² 5² 6² 7² 8² 9² 10²

1 4 9 16 25 36 49 64 81 100

Directions: Complete the table of squares.

11² 12² 13² 14² 15² 16² 17² 18² 19² 20²

121 144 169 196 225 256 289 324 361 400

Directions: Each square root is between two integers. Name the integers.1.

4, 52.

17, 18

3. 13, 14

4. 19, 20

5. 14, 15

6. 8, 9

7. 1, 2

8. 6, 7

Directions: Solve the following square roots.

9. 18

10.

11. 25

12.

13. 9

14.

Directions: Determine if the following numbers are rational or irrational. 15. R

16. I

17. I

18. R

19. Directions: Mark the position with a letter of each radical on the number line

2 1 0 1 2 3

c E F D B A

= 3

= 0= 2

= ½≈ 2.4 ≈ 1.7

Rational

Rational Irrational

Irrational


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Approximating Irrational Square Roots

1 4 9 16 25 36 49 64 81 100

121144 169196 225256289324361400

4 and 5

13 and 14

17 and 18

19 and 20

= 3

= 0= 2

= ½≈ 2.4 ≈ 1.7

= 15≈ 14.1

= 25= 11≈ 17.3

≈ 30.8

Perfect 2√

≈ 3.29 < 10 < 16√9 < √10 < √163 < 3.?? < 4

≈ 1.7

= 13.1

≈ 4.9

≈ 7.5

≈ 5.7

≈ 14.1

≈ 11.4

≈ 17.3

Key

2 3- rational irrational square roots approximating.notebook · 2019. 3. 27. · 2_3...

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