Using square roots to solve equations

Finding a square root to solve problems

Fluency and Practice - Lesson 23

Multiple Choice

$$\sqrt[]{64}$$ = ?

• 7

• 8

• 9

• 10

Multiple Choice

$$\sqrt[]{49}$$ = ?

• 7

• 8

• 9

• 10

Multiple Choice

$$\sqrt[]{100}$$ = ?

• 7

• 8

• 9

• 10

Multiple Choice

$$\sqrt[]{x^2}$$ = ?

• x

• 8

• $$x^2$$

• 100

The square root of any variable that is squared will be itself.

You can find the square root of numbers on both sides of the equal sign to keep the equation balanced

Solving for an unknown variable

Your answer can be positive or negative

Drag and Drop

$$x^2\ =100$$ ​ ​

Placeholder

Drag these tiles and drop them in the correct blank above

x = -10

Dropdown

How do I solve for y?

$$y^2\ =\ 81$$ ​

Select answer

Dropdown

How do I solve for b​

Select answer

? $$b^2\ =\ 25$$ ​

Dropdown

solve for b​

$$b^2\ =\ 25$$ ​​ ​

Select answer

Hint: There is one answer that is

Multiple Choice

Solve: $$x^2=\ 64$$

• x = -8

• x = 32

• x = $$\pm8$$

• x = 8

Multiple Choice

How do you solve: $$a^2\ =\ \frac{1}{49}$$

• $$\sqrt[]{a^2}=\sqrt[]{\frac{1}{49}}$$

• $$\sqrt[]{a^2}=\ \frac{1}{\sqrt[]{49}}$$

• $$\sqrt[]{a}=\sqrt[]{49}$$

• a = 49

Multiple Choice

Solve: $$a^2\ =\ \frac{1}{49}$$

• $$a\ =\ -\frac{1}{7}$$

• a = $$\frac{1}{7}$$

• a = 7

• $$a\ =\ \pm\frac{1}{7}$$

Multiple Choice

Solve: $$y^2=\ 81$$

• y = -9

• y = $$\frac{1}{9}$$

• $$y\ =\ \pm9$$

• y = $$-\frac{1}{9}$$

Match

Match the following

• $$-4^2=$$ ?

• $$-7^2\ =$$ ?

• $$-11^2$$ = ?

• $$-15^2$$ = ?

• $$-2^2$$ = ?

16

49

121

225

4

• 16

• 49

• 121

• 225

• 4

Multiple Choice

Solve: $$p^2\ =\frac{1}{121}$$

• p = -11

• p = $$-\ \frac{1}{11}$$

• $$p\ =\ \pm11$$

• $$p\ =\ \pm\frac{1}{11}$$

Multiple Choice

$$m^2\ =\ \frac{9}{16}$$

• m = $$\pm\frac{3}{4}$$

• p = $$\frac{9}{16}$$

• p = 9

• p = $$\frac{3}{4}$$

Match

Match the following

• $$\sqrt[]{16}$$

• $$\sqrt[]{36}$$

• $$\sqrt[]{196}$$

• $$\sqrt[]{169}$$

• $$\sqrt[]{1}$$

4 or -4

-6 or 6

-14 or 14

13 or -13

1 or -1

• 4 or -4

• -6 or 6

• -14 or 14

• 13 or -13

• 1 or -1

Multiple Choice

Solve: $$k^2\ =\ \frac{25}{144}$$

• k = 25

• k = 144

• k = $$\frac{5}{12}$$

• $$k\ =\ \pm\frac{5}{12}$$

​Up Next... 2 step equations

Multiple Choice

Let's try one:

What is the first step to solve this equation?

$$d^2\ -\ 2\ =\ 7$$

• find the square root of both sides

• subtract 2 from both sides

• add 2 to both sides

• subtract 7 from both sides

Multiple Choice

Let's try one:

What is the second step to solve this equation?

$$d^2\ -\ 2\ =\ 7$$

$$d^2\ =\ 9$$

• find the square root of both sides

• subtract 9 from both side

• add 9 to both sides

• square both sides

Multiple Choice

Let's try one:

Solve:

$$d^2\ -\ 2\ =\ 7$$

$$d^2\ =\ 9$$

• d = 9

• d = -3

• d = $$\pm9$$

• d = $$\pm3$$

Multiple Choice

Let's try one:

What is the first step to solve this equation?

$$f^2\ -\ 12\ =\ 132$$

• find the square root of both sides

• subtract 12 from both sides

• add 12 to both sides

• subtract 132 from both sides

Multiple Choice

Let's try one:

What is the second step to solve this equation?

$$f^2\ -\ 12\ =\ 132$$

$$f^2\ =\ 144$$

• divide both sides by 2

• combine like terms

• subtract 144 from both sides

• find the square root of both sides

Multiple Choice

Let's try one:

Solve:

$$f^2\ -\ 12\ =\ 132$$

$$f^2\ =\ 144$$

• f = 144

• f = $$\pm12$$

• f = -12

• f = 12

Math Response

What is the first step to solve this? $$x^2=256$$

Type answer here

Correct Answer: \sqrt{x^2}=\sqrt{256}

Deg^°

Rad

Poll

How comfortable are you with solving equations using squares and square roots?

• I'm still not really getting it

• I need some more practice but I'm starting to understand

• I'm pretty sure I can do some simple problems on my own

• I've got this! Give me the test!