Download (1.5) Square Roots. Compare and Order Real Numbers. Math 8

(1.5) Square Roots. Compare and Order Real Numbers.
Math 8
Numbers such as 1, 4, 9, 16, and 25 are called _________________, because they are squares of __________.
A ______________ of a number is one of its two equal factors. 4 · 4 = 16, so 4 is the _____________ of 16.
The symbol √
, called a __________________ , is used to show a __________________ square root.
Every positive number has TWO square roots: positive and negative.
Positive: √
Negative:
Since (5)² = 25, then √
√
Both roots: √
(–5)² = 25, then √
=5
√
= –5
= 5 = 5 and –5
What if it is not a perfect square?
The square root of a number that is not a perfect square falls between two _______________ whole numbers.
Step 1 Determine whether a number is a perfect square.
1. Is the number 29 a perfect square? Is there a whole number which can be squared to equal 29? _____
Step 2 Find the two consecutive whole numbers between which the √
lies.
2. The number 25 is the closest perfect square _________ than 29. What is √
3. The number 36 is closest perfect square greater than 29. What is √
4. √ lies between √
_____________
and √
? _____
? _____
. What are the two consecutive whole numbers between which √
lies?
Find the two consecutive whole numbers between which the square root of a given number lies.
Then circle the nearest integer.
√
√
_______ _______
Numbers like √
,√
,√
_______ _______
√
_______ _______
, … are called ______________________ ___________ . They have infinite amount of
digits after the decimal point without any obvious pattern of repeating digits.
Graph and order real numbers
Order numbers from least to greatest: , √ , √ , –2.5, √
Begin by graphing the numbers on the number line. Use a calculator to approximate irrational numbers.
-3
-2
-1
0
Read the numbers from left to right:
1
2
3
4