Download 1.5 Square Roots. Compare and order real numbers.

1.5 Square Roots. Compare and order real numbers.
Numbers such as 1, 4, 9, 16, and 25 are called perfect squares, because they are squares of whole numbers.
A square root _ of a number is one of its two equal factors. 4 · 4 = 16, so 4 is the square root of 16.
The symbol √
, called a radical sign , is used to show a POSITIVE 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 consecutive 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? No
Step 2 Find the two consecutive whole numbers between which the √
lies.
2. The number 25 is the closest perfect square _ less _ than 29. What is √
3. The number 36 is closest perfect square greater than 29. What is √
4. √
lies between √
and √
? _5__
? _ 6_
. What are the two consecutive whole numbers between which √
lies?
5 and 6
Find the two consecutive whole numbers between which the square root of a given number lies.
Then circle the nearest integer.
√
√
_4__ ___5___
__7____ __8____
√
__6____ ___7___
Numbers like √ , √ , √ , … are called irrational numbers . 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.
–2.5 √
-3
-2
√
-1
0
1
2
Read the numbers from left to right: –2.5, √ ,
√
3
,√ , √
4