9.1E: Exercises
- Page ID
- 30275
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Simplify Expressions with Square Roots
In the following exercises, simplify.
\(\sqrt{36}\)
- Answer
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6
\(\sqrt{4}\)
\(\sqrt{64}\)
- Answer
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8
\(\sqrt{169}\)
\(\sqrt{9}\)
- Answer
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3
\(\sqrt{16}\)
\(\sqrt{100}\)
- Answer
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10
\(\sqrt{144}\)
\(−\sqrt{4}\)
- Answer
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−2
\(−\sqrt{100}\)
\(−\sqrt{1}\)
- Answer
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−1
\(−\sqrt{121}\)
\(\sqrt{−121}\)
- Answer
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not a real number
\(\sqrt{−36}\)
\(\sqrt{−9}\)
- Answer
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not a real number
\(\sqrt{−49}\)
\(\sqrt{9+16}\)
- Answer
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5
\(\sqrt{25+144}\)
\(\sqrt{9}+\sqrt{16}\)
- Answer
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7
\(\sqrt{25}+\sqrt{144}\)
In the following exercises, estimate each square root between two consecutive whole numbers.
\(\sqrt{70}\)
- Answer
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\(8<\sqrt{70}<9\)
\(\sqrt{55}\)
\(\sqrt{200}\)
- Answer
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\(14<\sqrt{200}<15\)
\(\sqrt{172}\)
In the following exercises, approximate each square root and round to two decimal places.
\(\sqrt{19}\)
- Answer
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4.36
\(\sqrt{21}\)
\(\sqrt{53}\)
- Answer
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7.28
\(\sqrt{47}\)
Simplify Variable Expressions with Square Roots
In the following exercises, simplify.
\(\sqrt{y^2}\)
- Answer
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y
\(\sqrt{b^2}\)
\(\sqrt{a^{14}}\)
- Answer
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\(a^7\)
\(\sqrt{w^{24}}\)
\(\sqrt{49x^2}\)
- Answer
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\(7x\)
\(\sqrt{100y^2}\)
\(\sqrt{121m^{20}}\)
- Answer
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\(11m^{10}\)
\(25h^{44}\)
\(\sqrt{81x^{36}}\)
- Answer
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\(9x^{18}\)
\(\sqrt{144z^{84}}\)
\(−\sqrt{81x^{18}}\)
- Answer
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\(−9x^9\)
\(−\sqrt{100m^{32}}\)
\(−\sqrt{64a^2}\)
- Answer
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\(−8a\)
\(−\sqrt{25x^2}\)
\(\sqrt{144x^{2}y^{2}}\)
- Answer
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\(12xy\)
\(\sqrt{196a^{2}b^{2}}\)
\(\sqrt{169w^{8}y^{10}}\)
- Answer
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\(13w^{4}y^{5}\)
\(\sqrt{81p^{24}q^{6}}\)
\(\sqrt{9c^{8}d^{12}}\)
- Answer
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\(3c^{4}d^{6}\)
\(\sqrt{36r^{6}s^{20}}\)
Everyday Math
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
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
Why is there no real number equal to \(\sqrt{−64}\)?
- Answer
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Answers will vary.
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?