Square Root
Statement a = b2, means that ‘a’ is equal to the square of ‘b’. Also, we can conclude that ‘b’ is equal to the square-root of ‘a’.
if a and b are two numbers then,
[math]
a=b^2\\\\
or\; b =\sqrt{a}
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Example : Square root of 4 is 2.
Cube Root
Statement a = b3, means that ‘a’ is equal to the cube of ‘b’. Also, we can conclude that ‘b’ is equal to the cube-root of ‘a’.
if a and b are two numbers then,
[math]
a=b^3\\\\
or\; b =\sqrt[3]{a}
[/math]
Example : Cube root of 8 is 2.
Important Formulas
[math]
\sqrt{ab}\;=\;\sqrt{a}\;*\;\sqrt{b}
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[math]
\sqrt{\frac{a}{b}}\;=\;\frac{\sqrt{a}}{\sqrt{b}}
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Perfect square is an integer that is the square of an integer; in other words, it is the product of some integer with itself.
Example : 9 is a square number, since it can be written as 3 × 3.
There are two conditions for number to know if the number is perfect square :
- If the number ends with 1, 4, 5, 6, 9, then it is a perfect square.
- If the number ends with 2, 3, 7 and 8, then it is not a perfect square.
| Number, n | Value (sqrt-n) |
| 1 | 1 |
| 2 | 1.414 |
| 3 | 1.732 |
| 4 | 2 |
| 5 | 2.236 |
| 6 | 2.449 |
| 7 | 2.646 |
| 8 | 2.828 |
| 9 | 3 |
| 10 | 3.162 |
Now, let’s look at solved examples and exercises.
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