table of contents square roots of a quantity squared an important form of a square root is: it would...
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Table of Contents Recall that the absolute value of a negative number is the opposite of that number. We now define …TRANSCRIPT
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Square Roots of a Quantity Squared
2a
• An important form of a square root is:
It would seem that we should write …
2a a
… but as we shall see, this is not always the case.
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• Example 1
23 9 3
20 0 0
23 9 3
Note the patterns here.
Same
Same
Opposite in sign
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• Recall that the absolute value of a negative number is the opposite of that number.
23 3 3
We now define …
2a a
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• Example 2
Simplify
28 8 8
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• Example 3
Simplify
22x 2x
Since x + 2 could be negative for certain values of x, we must keep the absolute value sign.
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• Example 4
Simplify 12a
26a
First write the radicand as a quantity squared.
12a6a
Since 6a is always nonnegative, the absolute valuesign is not necessary.
6a
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• Example 5
Simplify 10a
25a
First write the radicand as a quantity squared.
10a5a
Since 5a would be negative if a were negative, the absolute value sign is necessary.
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• Example 6
Simplify 216 40 25x x
Try to create the pattern of 2a
To do this, factor the radicand.
216 40 25x x
24 5x
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Since 4x - 5 could be negative for certain values of x, we must keep the absolute value sign.
216 40 25x x
24 5x
4 5x
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• Sometimes the directions will include a statement that the values of the variables will be such that the radicand will be nonnegative.
• In this case, the absolute value sign is not necessary.
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• Example 7
Simplify the expression, assuming that the variable represents a nonnegative value.
10a
25a10a 5a
Since the variable can’t be negative, the absolute value sign is not necessary.
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