For more information, please see full course syllabus of Pre Algebra

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For more information, please see full course syllabus of Pre Algebra

For more information, please see full course syllabus of Pre Algebra

### Square Roots

- A square root is a number that, when multiplied by itself, is equal to the given number.
- For example, 5 and −5 are the square roots of 25. Multiply 5 times itself, 5•5 = 25. Multiply −5 • −5 = 25.
- The inverse of squaring is finding the square root.
- The square roots of a number are both the positive and negative value, they are opposites of each other.
- The symbol √ represents the positive square root of a number.

### Square Roots

√{49} =

7

− √{144} =

− 12

Estimate √{60} ≈

- 7 ×7 = 49
- 48 ×8 = 64

√{60} ≈ 8

Estimate − √{165} ≈

- ( − 12) ×( − 12) = 144
- ( − 13) ×( − 13) = 169

− √{165} ≈ − 13

You need to fence off 78 square feet of land. To the nearest ones place, about how long should each side be?

- √{78} ≈
- 8 ×8 = 64
- 9 ×9 = 81

≈ 9 feet

(√{25} )

^{2}=- (√{25} )(√{25} ) =
- 5 ×5 =

25

(√{100} )

^{2}=- (√{100} )(√{100} ) =
- 10 ×10 =

100

A square table has an area of 54 square feet. Estimate the length of each side of the table to the nearest foot.

- √{54} ≈
- 7 ×7 = 49
- 8 ×8 = 64

≈ 7 feet

Simplify the expression for y = 16.

− 8 − 3√y

− 8 − 3√y

- − 8 − 3√{16}
- − 8 − 3(4) =
- − 8 − 12 =

− 20

Simplify the expression for z = 9.

− √z + z

− √z + z

^{2}- − √9 + 9
^{2}= - − 3 + 81 =

78

*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.

Answer

### Square Roots

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

- Intro
- What You'll Learn and Why
- Vocabulary
- Square Roots
- Square Root Symbol
- Find the Square Root
- Estimating Square Roots
- Estimating Square Roots
- Simplifying Square Roots
- Extra Example 1: Estimate the Length
- Extra Example 2: Simplify the Expression
- Extra Example 3: Estimate the Length
- Extra Example 4: Simplify the Expression

- Intro 0:00
- What You'll Learn and Why 0:05
- Topics Overview
- Vocabulary 0:16
- Perfect Square
- Square Root
- Square Roots 1:13
- Every Positive Number has Two Square Roots
- Square Roots of a Number are Opposites
- Square Root Symbol 1:54
- Positive Square Root of a Number
- Compare: √25 and -√25
- Find the Square Root 2:50
- Example: Square Root of 81
- Example: Square Root of 121
- Estimating Square Roots 3:29
- Example: Square Root of 23
- Example: Square Root of 390
- Example: Negative Square Root of 125
- Estimating Square Roots 5:27
- Estimating Length
- Simplifying Square Roots 7:05
- Example: Square Root of 36
- Example: Simplifying Square Roots
- Extra Example 1: Estimate the Length 8:21
- Extra Example 2: Simplify the Expression 9:05
- Extra Example 3: Estimate the Length 9:50
- Extra Example 4: Simplify the Expression 10:34

2 answers

Last reply by: Professor Fung

Thu Dec 3, 2015 5:37 AM

Post by Jessie Carrillo on November 26, 2015

why is -16 to the second power= -256, isnt it -16 x -16= 256?

0 answers

Post by Nolan Bohler on April 29, 2014

In the practice questions! I think it's in the third practice question that I found this!

Estimate âˆš{60} â‰ˆ

Step 1. 7 Ã—7 = 49

Step 2. 48 Ã—8 = 64 <---------------Mistake or error? Isn't this suppose to be 8 x 8 which equals 64? And this is closer to (60) answer than 49??? Not 48 x 8 which equals of course (384)

Answer âˆš{60} â‰ˆ 8

1 answer

Last reply by: Professor Fung

Mon Sep 9, 2013 6:05 AM

Post by Saakshi Dhingra on September 3, 2013

So whenever we encounter an equation involving a negative infront of the number being squared, the negative only applies to final outcome, but not in the actual equation?

ex. -5squared= 5x5=25, then i would bring in the negative making it -25?

and i wouldnt do: -5x-5 (for the equation of above) making the anwser positive. =25

?