Answer: -√46 is between -7 and -6
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Explanation:
List out the perfect squares
- 1^2 = 1
- 2^2 = 4
- 3^3 = 9
- 4^2 = 16
- 5^2 = 25
- 6^2 = 36
- 7^2 = 49
- 8^2 = 64
and so on. We can see that 46 is between 6^2 = 36 and 7^2 = 49.
We can say 6^2 < 46 < 7^2
Applying the square root to all three sides leads us to 6 < sqrt(46) < 7
Now multiply all three sides by -1. This will flip the inequality signs
We go from
6 < sqrt(46) < 7
to
-6 > -sqrt(46) > -7
It might help to order things from smallest to largest to get this
-7 < -sqrt(46) < -6
This means -sqrt(46) is between -7 and -6 on the number line
See the diagram below.
