Square roots of perfect squares
Key Notes :
1. What is a Perfect Square?
- A perfect square is a number that can be expressed as the product of an integer with itself.
- Examples: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, etc.
2. What is a Square Root?
- The square root of a number is the value that, when multiplied by itself, gives the original number.
- The square root symbol is √.
- For example, √9 = 3, because 3 × 3 = 9.
3. Square Root of Perfect Squares
- The square root of a perfect square is always an integer.
- For example:
- √16 = 4 because 4 × 4 = 16
- √64 = 8 because 8 × 8 = 64
4. Finding Square Roots of Perfect Squares
- List the perfect squares up to 100: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100.
- Take the square root of these numbers:
- √1 = 1, √4 = 2, √9 = 3, √16 = 4, √25 = 5, and so on.
5. The Square Root Function
- The square root of a number can be found using the square root function (√x), where ‘x’ is the number whose square root you need to find.
- The square root of any positive perfect square is always a non-negative integer.
6. Examples
- √49 = 7 (because 7 × 7 = 49)
- √36 = 6 (because 6 × 6 = 36)
- √100 = 10 (because 10 × 10 = 100)
7. Key Properties
- The square root of any non-perfect square is irrational (e.g., √2, √3).
- The square root of 0 is 0: √0 = 0.
- Negative numbers do not have real square roots.
Learn with an example
What is √81?
You want to find the positive square root of 81
Figure out which number squared (multiplied by itself) equals 81 .
The number 9 squared equals 81 .
92=9.9=81
So √81 is 9
What is √9?
You want to find the positive square root of 9.
Figure out which number squared (multiplied by itself) equals 9.
The number3 squared equals 9 .
32 =3.3 = 9
So √9 is 3.
What is √100 ?
You want to find the positive square root of 100.
Figure out which number squared (multiplied by itself) equals 100.
The number10 squared equals 100 .
102 = 10 . 10 = 100
So √100 is 10.
Let’s try some problems!✍️