13.8.1E: Exercises
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Practice Makes Perfect
Simplify Expressions with Square Roots
In the following exercises, simplify.
Example \(\PageIndex{34}\)
\(\sqrt{36}\)
- Answer
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6
Example \(\PageIndex{35}\)
\(\sqrt{4}\)
Example \(\PageIndex{36}\)
\(\sqrt{64}\)
- Answer
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8
Example \(\PageIndex{37}\)
\(\sqrt{169}\)
Example \(\PageIndex{38}\)
\(\sqrt{9}\)
- Answer
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3
Example \(\PageIndex{39}\)
\(\sqrt{16}\)
Example \(\PageIndex{40}\)
\(\sqrt{100}\)
- Answer
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10
Example \(\PageIndex{41}\)
\(\sqrt{144}\)
Example \(\PageIndex{42}\)
\(−\sqrt{4}\)
- Answer
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−2
Example \(\PageIndex{43}\)
\(−\sqrt{100}\)
Example \(\PageIndex{44}\)
\(−\sqrt{1}\)
- Answer
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−1
Example \(\PageIndex{45}\)
\(−\sqrt{121}\)
Example \(\PageIndex{46}\)
\(\sqrt{−121}\)
- Answer
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not a real number
Example \(\PageIndex{47}\)
\(\sqrt{−36}\)
Example \(\PageIndex{48}\)
\(\sqrt{−9}\)
- Answer
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not a real number
Example \(\PageIndex{49}\)
\(\sqrt{−49}\)
Example \(\PageIndex{50}\)
\(\sqrt{9+16}\)
- Answer
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5
Example \(\PageIndex{51}\)
\(\sqrt{25+144}\)
Example \(\PageIndex{52}\)
\(\sqrt{9}+\sqrt{16}\)
- Answer
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7
Example \(\PageIndex{53}\)
\(\sqrt{25}+\sqrt{144}\)
In the following exercises, estimate each square root between two consecutive whole numbers.
Example \(\PageIndex{54}\)
\(\sqrt{70}\)
- Answer
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\(8<\sqrt{70}<9\)
Example \(\PageIndex{55}\)
\(\sqrt{55}\)
Example \(\PageIndex{56}\)
\(\sqrt{200}\)
- Answer
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\(14<\sqrt{200}<15\)
Example \(\PageIndex{57}\)
\(\sqrt{172}\)
In the following exercises, approximate each square root and round to two decimal places.
Example \(\PageIndex{58}\)
\(\sqrt{19}\)
- Answer
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4.36
Example \(\PageIndex{59}\)
\(\sqrt{21}\)
Example \(\PageIndex{60}\)
\(\sqrt{53}\)
- Answer
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7.28
Example \(\PageIndex{61}\)
\(\sqrt{47}\)
Simplify Variable Expressions with Square Roots
In the following exercises, simplify.
Example \(\PageIndex{62}\)
\(\sqrt{y^2}\)
- Answer
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y
Example \(\PageIndex{63}\)
\(\sqrt{b^2}\)
Example \(\PageIndex{64}\)
\(\sqrt{a^{14}}\)
- Answer
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\(a^7\)
Example \(\PageIndex{65}\)
\(\sqrt{w^{24}}\)
Example \(\PageIndex{66}\)
\(\sqrt{49x^2}\)
- Answer
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\(7x\)
Example \(\PageIndex{67}\)
\(\sqrt{100y^2}\)
Example \(\PageIndex{68}\)
\(\sqrt{121m^{20}}\)
- Answer
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\(11m^{10}\)
Example \(\PageIndex{69}\)
\(25h^{44}\)
Example \(\PageIndex{70}\)
\(\sqrt{81x^{36}}\)
- Answer
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\(9x^{18}\)
Example \(\PageIndex{71}\)
\(\sqrt{144z^{84}}\)
Example \(\PageIndex{72}\)
\(−\sqrt{81x^{18}}\)
- Answer
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\(−9x^9\)
Example \(\PageIndex{73}\)
\(−\sqrt{100m^{32}}\)
Example \(\PageIndex{74}\)
\(−\sqrt{64a^2}\)
- Answer
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\(−8a\)
Example \(\PageIndex{75}\)
\(−\sqrt{25x^2}\)
Example \(\PageIndex{76}\)
\(\sqrt{144x^{2}y^{2}}\)
- Answer
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\(12xy\)
Example \(\PageIndex{77}\)
\(\sqrt{196a^{2}b^{2}}\)
Example \(\PageIndex{78}\)
\(\sqrt{169w^{8}y^{10}}\)
- Answer
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\(13w^{4}y^{5}\)
Example \(\PageIndex{79}\)
\(\sqrt{81p^{24}q^{6}}\)
Example \(\PageIndex{80}\)
\(\sqrt{9c^{8}d^{12}}\)
- Answer
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\(3c^{4}d^{6}\)
Examlpe \(\PageIndex{81}\)
\(\sqrt{36r^{6}s^{20}}\)
Everyday Math
Example \(\PageIndex{82}\)
Decorating Denise wants to have a square accent of designer tiles in her new shower. She can afford to buy 625 square centimeters of the designer tiles. How long can a side of the accent be?
- Answer
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25 centimeters
Example \(\PageIndex{83}\)
Decorating Morris wants to have a square mosaic inlaid in his new patio. His budget allows for 2025 square inch tiles. How long can a side of the mosaic be?
Writing Exercises
Example \(\PageIndex{84}\)
Why is there no real number equal to \(\sqrt{−64}\)?
- Answer
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Answers will vary.
Example \(\PageIndex{85}\)
What is the difference between \(9^{2}\) and \(\sqrt{9}\)?
Self Check
ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.
ⓑ On a scale of 1–10, how would you rate your mastery of this section in light of your responses on the checklist? How can you improve this?