9.1 Simplify and Use Square Roots

Principal versus negative roots, why a negative radicand has no real value, estimating a root between whole numbers, and roots of variable expressions.

Elementary Algebra 2e, 9.1 Simplify and Use Square Roots

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61 exercises

9.1 Exercise 1

Before you get started, take this readiness quiz.

Simplify: ⓐ $9^{2}$ ⓑ $\left(−9\right)^{2}$ ⓒ $− 9^{2}$ .
If you missed this problem, review the reference.

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9.1 Exercise 2

Round 3.846 to the nearest hundredth.
If you missed this problem, review the reference.

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9.1 Exercise 3

For each number, identify whether it is a real number or not a real number:
ⓐ $− \sqrt{100}$ ⓑ $\sqrt{−100}$ .
If you missed this problem, review the reference.

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9.1 Exercise 4

Simplify: ⓐ $\sqrt{36}$ ⓑ $\sqrt{196}$ ⓒ $− \sqrt{81}$ ⓓ $− \sqrt{289}$ .

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9.1 Exercise 5

Simplify: ⓐ $− \sqrt{49}$ ⓑ $\sqrt{225}$ .

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9.1 Exercise 6

Simplify: ⓐ $\sqrt{64}$ ⓑ $− \sqrt{121}$ .

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9.1 Exercise 7

Simplify: ⓐ $\sqrt{−169}$ ⓑ $− \sqrt{64}$ .

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9.1 Exercise 8

Simplify: ⓐ $\sqrt{−196}$ ⓑ $− \sqrt{81}$ .

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9.1 Exercise 9

Simplify: ⓐ $− \sqrt{49}$ ⓑ $\sqrt{−121}$ .

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9.1 Exercise 10

Simplify: ⓐ $\sqrt{25} + \sqrt{144}$ ⓑ $\sqrt{25 + 144}$ .

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9.1 Exercise 11

Simplify: ⓐ $\sqrt{9} + \sqrt{16}$ ⓑ $\sqrt{9 + 16}$ .

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9.1 Exercise 12

Simplify: ⓐ $\sqrt{64 + 225}$ ⓑ $\sqrt{64} + \sqrt{225}$ .

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9.1 Exercise 14

Estimate the square root $\sqrt{38}$ between two consecutive whole numbers.

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9.1 Exercise 15

Estimate the square root $\sqrt{84}$ between two consecutive whole numbers.

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9.1 Exercise 16

Round $\sqrt{17}$ to two decimal places.

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9.1 Exercise 17

Round $\sqrt{11}$ to two decimal places.

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9.1 Exercise 18

Round $\sqrt{13}$ to two decimal places.

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9.1 Exercise 19

Simplify: ⓐ $\sqrt{x^{6}}$ ⓑ $\sqrt{y^{16}}$ .

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9.1 Exercise 20

Simplify: ⓐ $\sqrt{y^{8}}$ ⓑ $\sqrt{z^{12}}$ .

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9.1 Exercise 21

Simplify: ⓐ $\sqrt{m^{4}}$ ⓑ $\sqrt{b^{10}}$ .

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9.1 Exercise 22

Simplify: $\sqrt{16 n^{2}}$ .

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9.1 Exercise 23

Simplify: $\sqrt{64 x^{2}}$ .

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9.1 Exercise 24

Simplify: $\sqrt{169 y^{2}}$ .

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9.1 Exercise 25

Simplify: $− \sqrt{81 c^{2}}$ .

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9.1 Exercise 26

Simplify: $− \sqrt{121 y^{2}}$ .

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9.1 Exercise 27

Simplify: $− \sqrt{100 p^{2}}$ .

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9.1 Exercise 28

Simplify: $\sqrt{36 x^{2} y^{2}}$ .

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9.1 Exercise 29

Simplify: $\sqrt{100 a^{2} b^{2}}$ .

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9.1 Exercise 30

Simplify: $\sqrt{225 m^{2} n^{2}}$ .

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9.1 Exercise 31

Simplify: $\sqrt{64 p^{64}}$ .

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9.1 Exercise 32

Simplify: $\sqrt{49 x^{30}}$ .

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9.1 Exercise 33

Simplify: $\sqrt{81 w^{36}}$ .

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9.1 Exercise 34

Simplify: $\sqrt{121 a^{6} b^{8}}$

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9.1 Exercise 35

Simplify: $\sqrt{169 x^{10} y^{14}}$ .

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9.1 Exercise 36

Simplify: $\sqrt{144 p^{12} q^{20}}$ .

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9.1 Exercise 37

Simplify.

$\sqrt{36}$

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9.1 Exercise 39

Simplify.

$\sqrt{64}$

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9.1 Exercise 41

Simplify.

$\sqrt{9}$

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9.1 Exercise 43

Simplify.

$\sqrt{100}$

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9.1 Exercise 45

Simplify.

$− \sqrt{4}$

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9.1 Exercise 47

Simplify.

$− \sqrt{1}$

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9.1 Exercise 49

Simplify.

$\sqrt{−121}$

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9.1 Exercise 51

Simplify.

$\sqrt{−9}$

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9.1 Exercise 53

Simplify.

$\sqrt{9 + 16}$

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9.1 Exercise 55

Simplify.

$\sqrt{9} + \sqrt{16}$

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9.1 Exercise 57

Estimate each square root between two consecutive whole numbers.

$\sqrt{70}$

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9.1 Exercise 59

Estimate each square root between two consecutive whole numbers.

$\sqrt{200}$

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9.1 Exercise 61

Approximate each square root and round to two decimal places.

$\sqrt{19}$

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9.1 Exercise 63

Approximate each square root and round to two decimal places.

$\sqrt{53}$

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9.1 Exercise 65

Simplify.

$\sqrt{y^{2}}$

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9.1 Exercise 67

Simplify.

$\sqrt{a^{14}}$

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9.1 Exercise 69

Simplify.

$\sqrt{49 x^{2}}$

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9.1 Exercise 71

Simplify.

$\sqrt{121 m^{20}}$

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9.1 Exercise 73

Simplify.

$\sqrt{81 x^{36}}$

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9.1 Exercise 75

Simplify.

$− \sqrt{81 x^{18}}$

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9.1 Exercise 77

Simplify.

$− \sqrt{64 a^{2}}$

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9.1 Exercise 79

Simplify.

$\sqrt{144 x^{2} y^{2}}$

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9.1 Exercise 81

Simplify.

$\sqrt{169 w^{8} y^{10}}$

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9.1 Exercise 83

Simplify.

$\sqrt{9 c^{8} d^{12}}$

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9.1 Exercise 85

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?

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9.1 Exercise 87

Why is there no real number equal to $\sqrt{−64}$ ?

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