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Intermediate Algebra

Lynn Marecek

Chapter 8

Roots and Radicals - all with Video Answers

Educators


Section 1

Simplify Expressions with Roots

00:46

Problem 1

In the following exercises, simplify.
(a) $\sqrt{64}$ (b) $-\sqrt{81}$

Victor Salazar
Victor Salazar
Numerade Educator
00:34

Problem 2

In the following exercises, simplify.
(b) $\sqrt{169}$ (b) $-\sqrt{100}$

Nick Johnson
Nick Johnson
Numerade Educator
00:32

Problem 3

In the following exercises, simplify.
(C) $\sqrt{196}$ (C) $-\sqrt{1}$

Nick Johnson
Nick Johnson
Numerade Educator
00:31

Problem 4

In the following exercises, simplify.
(a) $\sqrt{144}$ (b) $-\sqrt{121}$

Nick Johnson
Nick Johnson
Numerade Educator
00:41

Problem 5

In the following exercises, simplify.
$\sqrt{\frac{4}{9}}$ (b) $-\sqrt{0.01}$

Nick Johnson
Nick Johnson
Numerade Educator
00:41

Problem 6

In the following exercises, simplify.
(a) $\sqrt{\frac{64}{121}}$ (.) $-\sqrt{0.16}$

Nick Johnson
Nick Johnson
Numerade Educator
00:38

Problem 7

In the following exercises, simplify.
(a) $\sqrt{-121}$ (b) $-\sqrt{289}$

Nick Johnson
Nick Johnson
Numerade Educator
00:41

Problem 8

In the following exercises, simplify.
(6) $-\sqrt{400}$ (b) $\sqrt{-36}$

Nick Johnson
Nick Johnson
Numerade Educator
00:33

Problem 9

In the following exercises, simplify.
a) $-\sqrt{225}$ (b) $\sqrt{-9}$

Nick Johnson
Nick Johnson
Numerade Educator
00:40

Problem 10

In the following exercises, simplify.
(a) $\sqrt{-49}$ (b) $-\sqrt{256}$

Nick Johnson
Nick Johnson
Numerade Educator
04:14

Problem 11

In the following exercises, simplify.
.(a) $\sqrt[3]{216}$ (b) $\sqrt[4]{256}$

DB
David Buchanan
Numerade Educator
02:57

Problem 12

In the following exercises, simplify.
(a) $\sqrt[3]{27}$ (b) $\sqrt[4]{16}$ (c) $\sqrt[5]{243}$

DB
David Buchanan
Numerade Educator
03:18

Problem 13

In the following exercises, simplify.
(a) $\sqrt[3]{512}$ (b) $\sqrt[4]{81}$ (c) $\sqrt[5]{1} \quad$

DB
David Buchanan
Numerade Educator
02:20

Problem 14

In the following exercises, simplify.
(a) $\sqrt[3]{125}$ (b) $\sqrt[4]{1296}$ (c) $\sqrt[5]{1024} \quad$

Teresa Fuston
Teresa Fuston
Numerade Educator
01:22

Problem 15

In the following exercises, simplify.
(a) $\sqrt[3]{-8}$ (b) $\sqrt[4]{-81}$ (c) $\sqrt[5]{-32}$

Teresa Fuston
Teresa Fuston
Numerade Educator
01:06

Problem 16

In the following exercises, simplify.

(a) $\sqrt[3]{-64}$
(b) $\sqrt[4]{-16}$
(c) $\sqrt[5]{-243}$

Teresa Fuston
Teresa Fuston
Numerade Educator
01:31

Problem 17

In the following exercises, simplify.

(a) $\sqrt[3]{-125}$
(6) $\sqrt[4]{-1296}$
(c) $\sqrt[5]{-1024}$

Teresa Fuston
Teresa Fuston
Numerade Educator
01:06

Problem 18

In the following exercises, simplify.

(a) $\sqrt[3]{-512}$
(b) $\sqrt[4]{-81}$
(c) $\sqrt[5]{-1}$

Teresa Fuston
Teresa Fuston
Numerade Educator
00:43

Problem 19

In the following exercises, estimate eoch raot between two cansecutive whole numbers.
.(a) $\sqrt{70}$ (b) $\sqrt[3]{71}$

Nick Johnson
Nick Johnson
Numerade Educator
00:52

Problem 20

In the following exercises, estimate eoch raot between two cansecutive whole numbers.
(a) $\sqrt{55}$ (b) $\sqrt[3]{119}$

Nick Johnson
Nick Johnson
Numerade Educator
00:40

Problem 21

In the following exercises, estimate eoch raot between two cansecutive whole numbers.
(a) $\sqrt{200}$ (b) $\sqrt[3]{137}$

Nick Johnson
Nick Johnson
Numerade Educator
00:42

Problem 22

In the following exercises, estimate eoch raot between two cansecutive whole numbers.
(a) $\sqrt{172}$ (b) $\sqrt[3]{200}$

Nick Johnson
Nick Johnson
Numerade Educator
01:04

Problem 23

In the following exercises, approximate each root and round to wo decimal places.
(a) $\sqrt{19}$ (b) $\sqrt[3]{89}$ (c) $4 \sqrt{97}$

Nick Johnson
Nick Johnson
Numerade Educator
01:01

Problem 24

In the following exercises, approximate each root and round to wo decimal places.
(a) $\sqrt{21}$ (b) $\sqrt[3]{93}$ (c) $\sqrt[4]{101}$

Nick Johnson
Nick Johnson
Numerade Educator
01:03

Problem 25

In the following exercises, approximate each root and round to wo decimal places.
. (a) $\sqrt{53}$ (b) $\sqrt[3]{147}$ (c) $\sqrt[4]{452}$

Erika Bustos
Erika Bustos
Numerade Educator
00:40

Problem 26

In the following exercises, approximate each root and round to wo decimal places.
(a) $\sqrt{47}$ (b) $\sqrt[3]{163}$ (c) $\sqrt[4]{527}$

Erika Bustos
Erika Bustos
Numerade Educator
01:15

Problem 27

In the foflowing exercises, simplify using absolute volues as necessary.
(a) $\sqrt[5]{u^5}$ (b) $\sqrt[8]{v^8}$

Erika Bustos
Erika Bustos
Numerade Educator
00:58

Problem 28

In the foflowing exercises, simplify using absolute volues as necessary.
(a) $\sqrt[3]{a^3}$ (b) $\sqrt[9]{b^9}$

Erika Bustos
Erika Bustos
Numerade Educator
01:02

Problem 29

In the foflowing exercises, simplify using absolute volues as necessary.
.(a) $\sqrt[4]{y^4}$ (b) $\sqrt[7]{m^7}$

Teresa Fuston
Teresa Fuston
Numerade Educator
01:05

Problem 30

In the foflowing exercises, simplify using absolute volues as necessary.
(a) $\sqrt[5]{k^8}$ (b) $\sqrt[6]{p^6}$

Teresa Fuston
Teresa Fuston
Numerade Educator
01:16

Problem 31

In the foflowing exercises, simplify using absolute volues as necessary.
(a) $\sqrt{x^6}$ (b) $\sqrt{y^{16}}$

Erika Bustos
Erika Bustos
Numerade Educator
01:13

Problem 32

In the foflowing exercises, simplify using absolute volues as necessary.
(a) $\sqrt{a^{14}}$ (b) $\sqrt{w^{24}}$

Erika Bustos
Erika Bustos
Numerade Educator
01:04

Problem 33

In the foflowing exercises, simplify using absolute volues as necessary.
(a) $\sqrt{x^{24}}$ (b) $\sqrt{y^{22}}$

Erika Bustos
Erika Bustos
Numerade Educator
00:59

Problem 34

In the foflowing exercises, simplify using absolute volues as necessary.
(a) $\sqrt{a^{12}}$ (b) $\sqrt{b^{26}}$

Erika Bustos
Erika Bustos
Numerade Educator
01:05

Problem 35

In the foflowing exercises, simplify using absolute volues as necessary.
(a) $\sqrt[3]{x^9}$ (b) $\sqrt[4]{y^{12}}$

Teresa Fuston
Teresa Fuston
Numerade Educator
00:58

Problem 36

In the foflowing exercises, simplify using absolute volues as necessary.
(a) $\sqrt[5]{a^{10}}$ (b) $\sqrt[3]{b^{27}}$

Vysakh M
Vysakh M
Numerade Educator
00:59

Problem 37

In the foflowing exercises, simplify using absolute volues as necessary.
(a) $\sqrt[4]{m^8}$ (b) $\sqrt[5]{n^{20}}$

Vysakh M
Vysakh M
Numerade Educator
02:07

Problem 38

In the foflowing exercises, simplify using absolute volues as necessary.
(a) $\sqrt[5]{r^{12}}$ (b) $\sqrt[3]{s^{30}}$

Teresa Fuston
Teresa Fuston
Numerade Educator
01:30

Problem 39

In the foflowing exercises, simplify using absolute volues as necessary.
(a) $\sqrt{49 x^2}$ (b) $-\sqrt{81 x^{18}}$

Vysakh M
Vysakh M
Numerade Educator
01:26

Problem 40

In the foflowing exercises, simplify using absolute volues as necessary.
(a) $\sqrt{100 y^2}$ (b) $-\sqrt{100 m^{32}}$

Vysakh M
Vysakh M
Numerade Educator
01:04

Problem 41

In the foflowing exercises, simplify using absolute volues as necessary.
(a) $\sqrt{121 m^{20}}$ (b) $-\sqrt{64 a^2}$

Vysakh M
Vysakh M
Numerade Educator
01:12

Problem 42

In the foflowing exercises, simplify using absolute volues as necessary.

(a) $\sqrt{81 x^{36}}$
(b) $-\sqrt{25 x^2}$

Vysakh M
Vysakh M
Numerade Educator
01:02

Problem 43

In the foflowing exercises, simplify using absolute volues as necessary.

(a) $\sqrt[4]{16 x^8}$
(b) $\sqrt[6]{64 y^{12}}$

Erika Bustos
Erika Bustos
Numerade Educator
01:29

Problem 44

In the foflowing exercises, simplify using absolute volues as necessary.

(a) $\sqrt[3]{-8 c^9}$
(b) $\sqrt[3]{125 d^{15}}$

Vysakh M
Vysakh M
Numerade Educator
01:23

Problem 45

In the foflowing exercises, simplify using absolute volues as necessary.

(a) $\sqrt[3]{216 a^6}$
(b) $\sqrt[5]{32 b^{20}}$

Vysakh M
Vysakh M
Numerade Educator
01:17

Problem 46

In the foflowing exercises, simplify using absolute volues as necessary.

(a) $\sqrt[7]{128 r^{14}}$
(6) $\sqrt[4]{81 s^{24}}$

Teresa Fuston
Teresa Fuston
Numerade Educator
01:54

Problem 47

In the foflowing exercises, simplify using absolute volues as necessary.

(a) $\sqrt{144 x^2 y^2}$
(b) $\sqrt{169 w^8 y^{10}}$
(c) $\sqrt[3]{8 a^{51} b^6}$

Vysakh M
Vysakh M
Numerade Educator
01:43

Problem 48

In the foflowing exercises, simplify using absolute volues as necessary.

(a) $\sqrt{196 a^2 b^2}$
(b) $\sqrt{81 p^{24} q^6}$
(c) $\sqrt[3]{27 p^{45} q^9}$

Vysakh M
Vysakh M
Numerade Educator
01:21

Problem 49

In the foflowing exercises, simplify using absolute volues as necessary.

(a) $\sqrt{121 a^2 b^2}$
(B) $\sqrt{9 c^8 d^{12}}$
(c) $\sqrt[3]{64 x^{15} y^{66}}$

Vysakh M
Vysakh M
Numerade Educator
01:33

Problem 50

In the foflowing exercises, simplify using absolute volues as necessary.

(a) $\sqrt{225 x^2 y^2 z^2}$
(b) $\sqrt{36 r^6 s^{20}}$
(c) $\sqrt[3]{125 y^{18} z^{27}}$

Vysakh M
Vysakh M
Numerade Educator
01:10

Problem 51

Why is there no real number equal to $V-64$ ?

Garrett Bess
Garrett Bess
Numerade Educator
00:27

Problem 52

What is the difference between $9^2$ and $\sqrt{9}$ ?

Elizabeth Xu
Elizabeth Xu
Numerade Educator
01:34

Problem 53

Explain what is meant by the $n^{\text {th }}$ root of a number.

Nick Johnson
Nick Johnson
Numerade Educator
03:03

Problem 54

Explain the difference of finding the $n^{\text {h }}$ root of a number when the index is even compared to when the index is odd.

Nick Johnson
Nick Johnson
Numerade Educator