Algebra 1 Common Core

Randall I. Charles,Basia Hall, Dan Kennedy

Chapter 10 Radical Expressions and Equations - all with Video Answers

Educators

Section 1

The Pythagorean Theorem

01:28

Problem 1

Find each missing side length.
(Graph cannot copy)

Vicki Stebbins

Numerade Educator

01:10

Problem 2

Find each missing side length.
(Graph cannot copy)

Vicki Stebbins

Numerade Educator

01:11

Problem 3

Could the lengths $12 \mathrm{cm}, 35 \mathrm{cm},$ and $37 \mathrm{cm}$ be the side lengths of a right triangle? Explain.

Vicki Stebbins

Numerade Educator

00:21

Problem 4

Vocabulary What is the converse of the conditional, "If you study math, then you are a student"?

Vicki Stebbins

Numerade Educator

00:39

Problem 5

Error Analysis A student found the length $x$ in the triangle at the right by solving the equation $12^{2}+13^{2}=x^{2}$ Describe and correct the error.

Vicki Stebbins

Numerade Educator

00:47

Problem 6

Use the triangle at the right. Find the missing side length. If necessary, round to the nearest tenth.
$$
a=3, b=4
$$

Vicki Stebbins

Numerade Educator

00:55

Problem 7

Use the triangle at the right. Find the missing side length. If necessary, round to the nearest tenth.
$$
a=6, c=10
$$

Vicki Stebbins

Numerade Educator

01:11

Problem 8

Use the triangle at the right. Find the missing side length. If necessary, round to the nearest tenth.
$$
b=1, c=\frac{5}{4}
$$

Vicki Stebbins

Numerade Educator

00:57

Problem 9

Use the triangle at the right. Find the missing side length. If necessary, round to the nearest tenth.
$$
a=5, c=13
$$

Vicki Stebbins

Numerade Educator

00:48

Problem 10

Use the triangle at the right. Find the missing side length. If necessary, round to the nearest tenth.
$$
a=0.3, b=0.4
$$

Vicki Stebbins

Numerade Educator

00:42

Problem 11

Use the triangle at the right. Find the missing side length. If necessary, round to the nearest tenth.
$$
a=8, b=15
$$

Vicki Stebbins

Numerade Educator

01:57

Problem 12

Use the triangle at the right. Find the missing side length. If necessary, round to the nearest tenth.
$$
a=1, c=\frac{5}{3}
$$

Vicki Stebbins

Numerade Educator

01:05

Problem 13

Use the triangle at the right. Find the missing side length. If necessary, round to the nearest tenth.
$$
b=6, c=7.5
$$

Vicki Stebbins

Numerade Educator

01:04

Problem 14

Use the triangle at the right. Find the missing side length. If necessary, round to the nearest tenth.
$$
b=3.5, c=3.7
$$

Vicki Stebbins

Numerade Educator

00:39

Problem 15

Use the triangle at the right. Find the missing side length. If necessary, round to the nearest tenth.
$$
a=1.1, b=6
$$

Vicki Stebbins

Numerade Educator

00:57

Problem 16

Use the triangle at the right. Find the missing side length. If necessary, round to the nearest tenth.
$$
a=8, c=17
$$

Vicki Stebbins

Numerade Educator

00:42

Problem 17

Use the triangle at the right. Find the missing side length. If necessary, round to the nearest tenth.
$$
a=9, b=40
$$

Vicki Stebbins

Numerade Educator

00:59

Problem 18

Use the triangle at the right. Find the missing side length. If necessary, round to the nearest tenth.
$$
b=2.4, c=7.4
$$

Vicki Stebbins

Numerade Educator

00:43

Problem 19

Use the triangle at the right. Find the missing side length. If necessary, round to the nearest tenth.
$$
a=4, b=7.5
$$

Vicki Stebbins

Numerade Educator

00:52

Problem 20

Use the triangle at the right. Find the missing side length. If necessary, round to the nearest tenth.
$$
a=0.9, c=4.1
$$

Vicki Stebbins

Numerade Educator

02:25

Problem 21

Fitness A jogger goes half a mile north and then turns west. If the jogger finishes $1.3 \mathrm{mi}$ from the starting point, how far west did the jogger go?

Vicki Stebbins

Numerade Educator

View

Problem 22

Construction A construction worker is cutting along the diagonal of a rectangular board $15 \mathrm{ft}$ long and $8 \mathrm{ft}$ wide. What will be the length of the cut?

Kathleen Carty

Numerade Educator

00:52

Problem 23

Determine whether the given lengths can be side lengths of a right triangle.
$$
15 \mathrm{ft}, 36 \mathrm{ft}, 39 \mathrm{ft}
$$

Vicki Stebbins

Numerade Educator

01:08

Problem 24

Determine whether the given lengths can be side lengths of a right triangle.
$$
12 \mathrm{m}, 60 \mathrm{m}, 61 \mathrm{m}
$$

Vicki Stebbins

Numerade Educator

01:01

Problem 25

Determine whether the given lengths can be side lengths of a right triangle.
$$
13 \mathrm{in} ., 35 \mathrm{in}, 38 \mathrm{in.}
$$

Vicki Stebbins

Numerade Educator

01:15

Problem 26

Determine whether the given lengths can be side lengths of a right triangle.
$$
16 \mathrm{cm}, 63 \mathrm{cm}, 65 \mathrm{cm}
$$

Vicki Stebbins

Numerade Educator

00:52

Problem 27

Determine whether the given lengths can be side lengths of a right triangle.
$$
14 \mathrm{in} ., 48 \mathrm{in} ., 50 \mathrm{in.}
$$

Vicki Stebbins

Numerade Educator

00:50

Problem 28

Determine whether the given lengths can be side lengths of a right triangle.
$$
16 \mathrm{yd}, 30 \mathrm{yd}, 34 \mathrm{yd}
$$

Vicki Stebbins

Numerade Educator

01:47

Swimming A swimmer asks a question to a lifeguard sitting on a tall chair, as shown in the diagram. The swimmer needs to be close to the lifeguard to hear the answer. What is the distance between the swimmer's head and the lifeguard's head?

Vicki Stebbins

Numerade Educator

01:01

Problem 30

Any set of three positive integers that satisfies the equation $a^{2}+b^{2}=c^{2}$ is a Pythagorean triple. Determine whether each set of numbers is a Pythagorean triple.
$$
11,60,61
$$

Vicki Stebbins

Numerade Educator

00:55

Problem 31

Any set of three positive integers that satisfies the equation $a^{2}+b^{2}=c^{2}$ is a Pythagorean triple. Determine whether each set of numbers is a Pythagorean triple.
$$
13,84,85
$$

Vicki Stebbins

Numerade Educator

01:00

Problem 32

Any set of three positive integers that satisfies the equation $a^{2}+b^{2}=c^{2}$ is a Pythagorean triple. Determine whether each set of numbers is a Pythagorean triple.
$$
40,41,58
$$

Vicki Stebbins

Numerade Educator

01:01

Problem 33

Any set of three positive integers that satisfies the equation $a^{2}+b^{2}=c^{2}$ is a Pythagorean triple. Determine whether each set of numbers is a Pythagorean triple.
$$
50,120,130
$$

Vicki Stebbins

Numerade Educator

00:54

Problem 34

Any set of three positive integers that satisfies the equation $a^{2}+b^{2}=c^{2}$ is a Pythagorean triple. Determine whether each set of numbers is a Pythagorean triple.
$$
32,126,130
$$

Vicki Stebbins

Numerade Educator

00:51

Problem 35

Any set of three positive integers that satisfies the equation $a^{2}+b^{2}=c^{2}$ is a Pythagorean triple. Determine whether each set of numbers is a Pythagorean triple.
$$
28,45,53
$$

Vicki Stebbins

Numerade Educator

01:43

Problem 36

Think About a Plan A banner shaped like a right triangle has a hypotenuse of length $26 \mathrm{ft}$ and a leg of length $10 \mathrm{ft}$. What is the area of the banner?
What information do you need to find the area of a triangle?
How can you find the length of the other leg?

Vicki Stebbins

Numerade Educator

01:04

Problem 37

History Originally, each face of the Great Pyramid of Giza was a triangle with the dimensions shown. How far was a corner of the base from the pyramid's top? Round to the nearest foot.

Vicki Stebbins

Numerade Educator

01:57

Problem 38

Two sides of a right triangle measure 10 in. and 8 in.
a. Writing Explain why this is not enough information to be sure of the length of the third side.
b. Give two possible values for the length of the third side.

Vicki Stebbins

Numerade Educator

01:10

Problem 39

Physics If two forces pull at right angles to each other, the resultant force can be represented by the diagonal of a rectangle, as shown at the right. This diagonal is a hypotenuse of a right triangle. 50 -lb force and a 120 -lb force combine for a resultant force of $130 \mathrm{lb}$. Are the forces pulling at right angles to each other? Explain.

Vicki Stebbins

Numerade Educator

01:18

Problem 40

A rectangular box is 4 cm wide, 4 cm tall, and 10 cm long. What is the diameter of the smallest circular opening through which the box will fit? Round to the nearest tenth of a centimeter.

Vicki Stebbins

Numerade Educator

03:13

Problem 41

Reasoning Use the diagram at the right.
a. Find the area of the larger square. Write your answer as a trinomial.
b. Find the area of the smaller square.
c. Find the area of each triangle in terms of $a$ and $b .$
d. The area of the larger square equals the sum of the area of the smaller square and the areas of the four triangles. Write this equation and simplify. What do you notice?

Vicki Stebbins

Numerade Educator

03:52

Problem 42

Geometry The lengths of the sides of a right triangle are three consecutive integers. Write and solve an equation to find the three integers.

Vicki Stebbins

Numerade Educator

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

Problem 13

Problem 14

Problem 15

Problem 16

Problem 17

Problem 18

Problem 19

Problem 20

Problem 21

Problem 22

Problem 23

Problem 24

Problem 25

Problem 26

Problem 27

Problem 28

Problem 29

Problem 30

Problem 31

Problem 32

Problem 33

Problem 34

Problem 35

Problem 36

Problem 37

Problem 38

Problem 39

Problem 40

Problem 41

Problem 42