Squares and Square Roots with Negatives and Fractions

Solving Square Roots

EXPLORATION!

Multiple Choice

Find the area of this square

• 16 cm

• $$16\ cm^2$$  

• 8cm

• $$8\ cm^2$$  

Multiple Choice

Find the area of this square.

• 49 mi

• 14 mi

• $$14\ mi^2$$  

• $$49\ mi^2$$  

Multiple Choice

Find the area of this square.

• 282.24 in

• $$33.6\ in^2$$  

• $$282.24\ in^2$$  

• 33.6 in

Multiple Choice

Who is He?

• Spongebob

• Squidward

• Sandy

• My leg! Guy

Square

1. "To square" 5. 5x5 = 25

2. Square 4. 4x4=16

3. "Square it" aka square that number.

​Example

• Means to multiply a number by itself

• "Squaring" is the same as raising that number or variable to the power of 2.

The square of a number is the same as the square of its additive inverse.

Multiple Choice

8²

• 16
• 8
• 64²
• 64

Multiple Choice

What is 0.4²

• 0.16

• 1.6

Multiple Choice

$$\left(-2\right)^2$$

• 2
• 4
• 0
• -4

Multiple Choice

$$-12^2$$

• 0
• -144
• 144

• 169

Multiple Choice

$$-12.2^2$$

• -148.84

• 121.2
• 169.64
• -144.4

Multiple Choice

From A movie we probably all seen

• Big ogre

• Shrek

• Donkey and Ogre Adventures

• BIg Booger

Perfect Squares

Perfect Squares

Multiplying an integer by itself.

ARE ONLY POSITIVE!!!
Think of it as squaring the absolute value of the integer.
They can also be the product negative integers. Like (-6) x (-6) = 36

Multiple Choice

1- Which number is a perfect square?

• a) 32

• b) 25

• c) 22

• D) 24

Multiple Choice

3- Which number is perfect square?

• a) 36

• b) 39

• c) 89

• d) 11

Multiple Choice

4- Which number is a perfect square?

• a) 100

• b) 110

• c) 120

• d) 59

Multiple Choice

5- Which number is perfect square?

• a) 124

• b) 144

• c) 158

• d) 164

Multiple Choice

6-Which number is perfect square?

• a) 1

• b) 2

• c) 5

• d) 8

Multiple Choice

12- Which number is perfect square?

• a) 4

• b) 44

• c) 34

• d) 54

Multiple Choice

We all know her

• Peppa PIg

• Talking Pig

• Clothed Pig

• Piggy Family

Square roots

​Is the opposite of squares

Square roots continued

​Is the opposite of squares

Square roots continued

Multiple Choice

$$\sqrt[]{9}$$

• 7
• 3
• 4
• 6

Multiple Choice

$$\sqrt[]{100}$$

• 5
• 10
• 12
• 15

Multiple Choice

$$\sqrt[]{81}$$

• 15
• 9
• 12
• 7

Multiple Choice

Who is this famous hedgehog?

• Tron

• Sonic

• George

• Henry

Square roots continued

Multiple Choice

$$-\ \sqrt[]{144}$$

• -6
• 24
• 0
• -12

Multiple Choice

$$-\ \sqrt[]{36}$$

• -6
• 9
• 0
• -3

Multiple Choice

Name this cartoon character who lives under the sea.

• Jacob Star

• Patrick Star

• Jordan Star

• Theodore Star

Multiple Choice

Solve the equation. $$x^2\ =\ 121$$

• x = ±11
• x = ±13
• x = ±10
• x = ±12

Multiple Choice

Solve the equation. $$x^2\ =\ 64$$

• x = ±4
• x = ±16
• x = ±8
• x = ±32

Multiple Choice

Solve the equation. $$x^2\ =\ 169$$

• x = ±15
• x = ±13
• x = ±14
• x = ±12

Multiple Choice

Name this cartoon character.

• Meg Griffin

• Kimpossible

• Dora the Explorer

• Mrs. Frizzle

Simplifying Radicals

A square root is simplified when...

1. There's no perfect square(s) in the radicand.
2. There's no fraction in the radicand.
3. There's no radical in the denominator of a fraction.

Simplifying- To find another expression with the same value.

Steps:
1. Rewrite the square root with the largest perfect square factor.
2. Rewrite the square root.
3. Find the perfect square of the factor(s) (square root the perfect squares).
4. Move the perfect squares outside the radical.

Steps:
1. Rewrite the square root with the largest perfect square factor.
2. Rewrite the square root.
3. Find the perfect square of the factor(s) (square root the perfect squares).
4. Move the perfect squares outside the radical.

Multiple Choice

Simplify  $$\sqrt[]{50}$$

• $$5\ \sqrt[]{2}$$

• $$3\ \sqrt[]{16}$$

• $$2\ \sqrt[]{25}$$

• $$10\ \sqrt[]{5}$$

Multiple Choice

Simplify: $$\sqrt[]{96}$$

• $$4\ \sqrt[]{6}$$

• $$3\ \sqrt[]{6}$$

• $$6\ \sqrt[]{5}$$

• $$6\ \sqrt[]{8}$$

Multiple Choice

Simplify: $$\sqrt[]{24}$$

• $$2\ \sqrt[]{6}$$

• $$4\ \sqrt[]{6}$$

• $$2\ \sqrt[]{12}$$

• $$3\ \sqrt[]{8}$$

Multiple Choice

Simplify.

• A
• B
• C
• D

Multiple Choice

What about this one?

• Yotube

• Youtobe

• Youtube

• tv

Steps:
1. Rewrite the square root with the largest perfect square factor.
2. Rewrite the square root.
3. Find the perfect square of the factor(s) (square root the perfect squares).
4. Move the perfect squares outside the radical.
5. Multiply the integers outside the radical with the integers that were moved from under the radical.

Steps:
1. Rewrite the square root with the largest perfect square factor.
2. Rewrite the square root.
3. Find the perfect square of the factor(s) (square root the perfect squares).
4. Move the perfect squares outside the radical.
5. Multiply the integers outside the radical with the integers that were moved from under the radical.

Multiple Choice

Simplify: $$3\ \sqrt[]{27}$$

• 9
• $$9\ \sqrt[]{3}$$

• $$3\ \sqrt[]{9}$$

• 3

Multiple Choice

• Xbox One
• Wii
• Xbox
• NONE

Multiple Choice

Simplify $$2\ \sqrt[]{12}$$

• $$4\ \sqrt[]{3}$$

• $$6\ \sqrt[]{5}$$

• $$6\ \sqrt[]{3}$$

• $$8\ \sqrt[]{3}$$

Multiple Choice

Simplify.

• A

• B

• C

• D

Multiple Choice

Simplify $$\sqrt{500}$$  

• $$4\sqrt{125}$$  

• $$5\sqrt{10}$$  

• $$10\sqrt{5}$$  

• $$10\sqrt{50}$$  

Multiple Choice

What logo is this

• Targe
• Target
• targey
• tigger

Steps:
1. Rewrite the numerator and denominator with a radical.
2. Find the square root of the numerator and denominator.

Multiple Choice

Simplify: $$\frac{\sqrt{4}}{\sqrt{121}}$$  

• $$\frac{4}{11}$$  

• $$\frac{\sqrt{484}}{121}$$  

• $$\frac{2}{11}$$  

• $$\frac{2\sqrt{121}}{121}$$  

Multiple Choice

Simplify

$$\sqrt{\frac{169}{400}}$$  

• $$\frac{16}{40}$$  

• $$\frac{14}{20}$$  

• $$\sqrt{\frac{169}{400}}$$  

• $$\frac{13}{20}$$  

Multiple Choice

Name this logo

• Buffalos
• Buffalo Wild Wings

Steps:
1. Rewrite the numerator and denominator with a radical.
2. "rationalize the denominator"- Remove a radical from the denominator.
Multiply the numerator and the denominator by the radical in the denominator.
3. You can only multiply the numbers under the radicals by each other.

Multiple Choice

Rationalize the denominator: $$\frac{\sqrt{5}}{\sqrt{6}}$$  

• $$\sqrt{5}$$  

• $$\frac{\sqrt{30}}{6}$$  

• $$\frac{\sqrt{5}}{6}$$  

• $$\frac{\sqrt{30}}{36}$$  

Multiple Choice

Rationalize the denominator:
$$\sqrt{\frac{3}{10}}$$  

• $$\frac{\sqrt{3}}{10}$$  

• $$\frac{\sqrt{3}}{100}$$  

• $$\frac{\sqrt{30}}{10}$$  

• $$10\sqrt{3}$$  

Multiple Choice

Rationalize the denominator.

$$\frac{4}{\sqrt{5}}$$  

• $$\frac{4\sqrt{5}}{5}$$  

• $$\frac{\sqrt{5}}{4}$$  

• $$\frac{\sqrt{6}}{3}$$  

• $$\frac{5\sqrt{2}}{2}$$  

If needed simplify your fractions with the numbers outside the radicals.

Multiple Choice

$$\frac{3\sqrt{5}}{\sqrt{3}}$$  Fully simplify....

Multiple Choice

Simplify:

• 2
• 4√3
• 2√3
• 4

Multiple Choice

• A
• B
• C
• D