Main content

## Pre-algebra

### Unit 11: Lesson 1

Square roots & cube roots- Intro to square roots
- Square roots of perfect squares
- Square roots
- Intro to cube roots
- Cube roots
- Worked example: Cube root of a negative number
- Equations with square roots & cube roots
- Square root of decimal
- Roots of decimals & fractions
- Equations with square roots: decimals & fractions
- Dimensions of a cube from its volume
- Square and cube challenge
- Square roots review
- Cube roots review

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# Square roots of perfect squares

CCSS.Math:

Learn how to find the square root of perfect squares like 25, 36, and 81.

Let's start by taking a look at an example evaluating the square root of start color #1fab54, 25, end color #1fab54:

**Step 1:**Ask, "What number squared equals start color #1fab54, 25, end color #1fab54?"

**Step 2:**Notice that start color #11accd, 5, end color #11accd squared equals start color #1fab54, 25, end color #1fab54.

**The answer**

Here's a question to make sure you understood:

# Connection to a square

Finding the square root of start color #1fab54, 25, end color #1fab54 is the same as finding the side length of a square with an area of start color #1fab54, 25, end color #1fab54.

A square with an area of start color #1fab54, 25, end color #1fab54 has a side length of start color #11accd, 5, end color #11accd.

# Practice Set 1:

### Reflection question

# Practice Set 2:

# Practice Set 3:

## Want to join the conversation?

- is this 8th-grade math?

im in 5th grade:+(5 votes)- That is awesome for you continue to learn ahead(23 votes)

- How can we use square roots in life?(6 votes)
- There are many ways in life you can use square roots. Some of them include a mathmatician, engineer, architect, carpenter, etc.(3 votes)

- Would you do the same for a negative square root ?🤔(2 votes)
- You cannot find the negative square root of a number. Think of what square roots are. If we take 36 and find the square root, you'll see it's 6. Because 6 x 6 = 36. We multiply it by itself and it gives us 36.

We can't do this with negatives. Consider -36 and finding the square root of that. Which number multiplied by itself will get -36?

Well, remember the rules we have for multiplying negatives and positives.

negative x negative = positive

negative x positive = positive

positive x positive = positive.

It can't be -6, because that will give us a positive number, instead of -36.

It can't be 6, because that will also give us a positive number instead of -36.

So, negatives can't have square roots.

You'll learn in more advanced classes what we do in these cases.(8 votes)

- can a decimal have a square root(4 votes)
- Yes, decimals can have square roots. For example, the (principal) square root of 0.64 is 0.8, since 0.8*0.8 = 0.64.(3 votes)

- How to calculate imperfect squares?(3 votes)
- imperfect square roots (example: 32 SQUARE)(I am going to do square uppercased because I don't know how to make a square root sign)

32 SQUARE

start with the number you think is closest to this number

25 SQUARE

than the other closest

36 SQUARE

than just find the root of these numbers

5

6

it is between 5 and 6

hope this helped and may God bless your day(5 votes)

- If I take a times table and I start to go across down I'll get the square roots right?

1,4,9,16,25,36...(4 votes) - How do you estimate square roots?(3 votes)
- Using the exponent of whole numbers, you can estimate square roots.

For example, √39 is a little bigger than 6 squared, which is 36, and it is smaller than 7 squared, which is 49. We can estimate √39 to be between 6 and 7, a little closer to 6.

Hope this helped you.(2 votes)

- How do we know if the answer is positive of negative? e.g. 9 = 3^2 or 9 = -3^2. Are both answers acceptable?(2 votes)
- Many times you will see something like this √9 = ±3. The "±" is pronounced "plus or minus" and you will see it in things like quadratic formula. But, sometimes both answers are NOT acceptable. For example, if you are using the pythagorean theorem and trying to get a side length, a negative answer won't work (you cannot have a negative side length). Other scenarios in which you can determine is when you simply know what sign the answer is supposed to be in.(3 votes)

- Is there an equation to find the square root of a number? (Ex: Evaluate the square root of 81; I know that it's 9, but would there be a way to find out if it was a larger number that I didn't know the answer to?)(3 votes)
- can a negative become a positive by an exponent?(2 votes)
- Not quite the right question, but in multiplying (and thus exponents) the number of negatives determines the sign of the answer, so even number of negatives (or even exponents) gives positive answer, negative number (odd exponents give negative answer)

So (-2)^2=4 (-2)^3=-8 (-2)^4=16, (-2)^5=-32(3 votes)