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### Course: 8th grade>Unit 1

Lesson 4: Approximating irrational numbers

# Approximating square roots to hundredths

Let's approximate the square root of 45 without a calculator. We'll explore how to find the perfect squares around 45 and use them to make an educated guess. Then, we'll refine our guess by squaring it to see how close we get to 45. Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

• What are the differences between square roots and cube roots?
• The cube root is the original number to the third power as an example, 3. 3 squared is 9. but nine times 3 or 3 cubed is 27. the cube root is 3 because 3*3*3=27.
• what is a perfect square and what does it mean?
• A perfect square is a number that can be expressed as the product of two equal integers.

Examples of perfect squares:
* 9
o 9 is a perfect square becuase it can be expressed as 3 * 3 (the product of two equal integers)
* 16
o 16 is a perfect square becuase it can be expressed as 4 * 4 (the product of two equal integers)
* 25
o 25 is a perfect square becuase it can be expressed as 5 * 5 (the product of two equal integers)

NON examples of perfect squares:

… (more) * 8
o 8 is a not perfect square because you cannot express it as the product of two equal integers
* 5
o 5 is a not perfect square because it cannot be expressed as the product of two equal integers
* 7
o 7 is a not perfect square because you cannot express it as the product of two equal integers

hope this helps :)
• at what does he mean by "nine of the way through it? Please help
• Take the distance from 36 to 49. that difference is 13 (49-36=13)
Next take the distance from 36 to 45. that difference 9.
So when you are going from 36 to 49, you will arrive at 45 at when you have completed nine 16ths of the trip.
• What is the difference between square roots and cube roots
• Squaring a number multiplies twice. Some squared numbers:
1² = 1 * 1
2² = 2 * 2
3² = 3 * 3
4² = 4 * 4
5² = 5 * 5
Cubing a number multiplies three times. Some cubed numbers:
1³ = 1 * 1 * 1
2³ = 2 * 2 * 2
3³ = 3 * 3 * 3
4³ = 4 * 4 * 4
5³ = 5 * 5 * 5
And so on.
But when we take the ROOT of a number, what we are actually doing is asking a question. When we get the square root of a number we are asking, "What number times what number equals the number we are squaring?" For example:
√4 = 2
The square root of 4 equals 2. Why? Because 2 times 2 equals 4. Another example:
√9 = 3
The square root of 9 equals 3. Why? Because 3 times 3 equals 9.
Now, the difference between square roots and cube roots is that with cube roots, we are asking a similar question, but the amount that the numbers need to multiply changes.
³√8 = 2
The cube root of 8 equals 2. Why? Because 2 times 2 times 2 equals 8. Another example:
³√27 = 3
The cube root of 27 equals 3. Why? Because 3 times 3 times 3 equals 27.
I hope you were able to understand and get through all that! It was a rather hefty manuscript. :)
Toodleoo! *tips hat*
• why not just use Desmos calculator
• probably because if they allowed calculators people could just solve it with a built-in square root function and not have any actual knowledge of how it works (like what you seem to be suggesting), also, things like Desmos (and really, modern technology in general) only exist because people did math to find accurate and efficient ways to calculate things like this
• How does he get 9/13
• The difference between 36 and 49 is 13, and 45 is 9 greater than 36, so it’s 9/13 of the way from 36 to 49
• how did he get the 9 in 9/13?
• Hello!

Do you understand the part where Sal says that 45 (and the square root of 45) is halfway between 49 (and the square root of 49) and 36 (and the square root of 36)?

At , Sal explains that the difference between 49 and 45 is 4, and that the difference between 45 and 36 is 9. Therefore, the difference between 49 and 36 is 13.

He then puts the 9 above the 13 to get 9/13!

This was confusing for me too, but I hope this helped!
• I do not think many of us are taking into account that finding square roots is just the opposite of finding the area of a square, And finding cube roots is just the opposite of finding the volume of a cube. You all may know this, but if you didn't, I hope you find this unit easier with your newfound knowledge!
• i still don't understand...