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8. −(−2) 4
9. (10) 0
10. (−23) 0
11. (−1) 59
12. 0 0
2.8 Square Roots and Signed Numbers
Recall that a number whose square is N is called a square root of N. 6 is a square root of 36, because
2
6 =36. −6 is also a square root of 36, since the product of two numbers with the same sign is positive:
2
(−6) =36.
In general,
Every positive number N has two square roots, which are
opposites:
√
• The positive square root is denoted N.
√
• The negative square root is − N.
As usual, 0 is a special case. It has only one square root, itself:
√
0= 0.
√
Example 72. Between what two consecutive integers does − 19 lie?
2
2
Solution. 19 is greater than 4 but less than 5 .It follows that
√
4 < 19 < 5.
The “mirror image” of this relationship on the negative half of the number line is
√
−5 < − 19 < −4,
√
that is, − 19 is greater than −5but less than −4, as indicated below.
√ √
− 19 19
| | | | | | | | | | |
−5 −4 −3 −2 −1 0 1 2 3 4 5
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