approximating roots
DESCRIPTION
Approximating Roots. Units 1.12 & 1.13. Approximating Square Roots: Numbers that are not perfect squares do not have integer square roots. You can use perfect squares to approximate the square root of a number that is not a perfect square. - PowerPoint PPT PresentationTRANSCRIPT
Approximating RootsUnits 1.12 & 1.13
Approximating Square Roots: Numbers that are not perfect squares do not have integer square roots. You can use perfect squares to approximate the square root of a number that is not a perfect square.
Step 1: Locate the closest perfect squares (one smaller, one bigger). Step 2: Decide which is actually closer to the desired radicand.
Example: Estimate . Since 52 is not a perfect square, we need to find two perfect squares that are close to 52. They are:
49 and 64 because or .
So, lies between 7 and 8. And since 52 is closer to 49, we know that is closer to 7.
Try it!
Estimate each square
root.Closer to 9
1)
Closer to 12
Try it!
Estimate each square
root.
2)
Closer to 10
practice it!
Estimate each square
root.
3)
practice it!
Estimate each square
root.Closer to -9
4)
Get goodat it!
Estimate each square
root.Closer to -14
5)
Closer to 5
Get goodat it!
Estimate each cube
root.
6)
Closer to 10
Get goodat it!
Estimate each cube
root.
7)
Closer to –7
Get goodat it!
Estimate each cube
root.
8)
HOMEWORK TIME Approximating Roots 1 WS: 1-21 only
LET’S GET CLOSER!Now it’s time to approximate to one decimal place!
Approximating Square Roots to one decimal place: Now that we can approximate square roots to between two integers, let’s get a little closer!
Step 1: Determine between what two integers the root lies and decide which is closer.
Step 2: Make educated guesses to 1 decimal place & try them!
Step 3: Decide which is closer!
Example: Approximate to one decimal place.Step 1: We know that it lies between 7 and 8 from our previous
example—and that it is closer to 7. Step 2: Since it is closer to 7… let’s try 7.2, …
What is 7.22? 7.32? Which is better?
Example: Approximate to one decimal place.Step 1: We know that it lies between 7 and 8 from our previous
example—and that it is closer to 7. Step 2: Since it is closer to 7… let’s try 7.1, …
What is 7.12? 7.22? Which is better? Closer to 7.2Step 3: Decide which is closer!
Try it!
Approximate to one decimal place.
Closer to 9
9)
Closer to 9.3
Try it!
Approximate to one decimal place.
Closer to 12
10)
Closer to 11.7
Closer to 10
practice it!
Approximate to one
decimal place.
11)
Closer to 10.4
Closer to –9
practice it!
Approximate to one
decimal place.
12)
Closer to -8.7
Closer to 5
13)
Closer to 4.8
New!Get goodat it!
Approximate to one decimal place.
Closer to –11
14)
Closer to -10.9
New!Get goodat it!
Approximate to one decimal place.
Let’s Get Closer!Now it’s time to approximate to two decimal places!
Approximating Roots to two decimal places:
Example: Approximate to two decimal places.Step 1: We know that it lies between 7.2 and 7.3 from our
previous example—and that it is closer to 7.2. Step 2: Since it is closer to 7.2… let’s try 7.21, 7.22, & 7.23!
Closer to 7.21
Try it!
Approximate to two decimal places.
15)
Closer to 9.3
Closer to 9.33
Try it!
Approximate to two decimal places.
16)
Closer to 10.4
Closer to 10.44
17) New!
Closer to 7.75
practice it!
Approximate to two
decimal places.
18)
Closer to -7.44
New!Get goodat it!
Approximate to two decimal places.
19)
Closer to 8.69
New!Get goodat it!
Approximate to two decimal places.
HOMEWORK TIME Approximating Roots 2 WS