Square Root Formula (original) (raw)
Last Updated : 28 Jan, 2026
The square root of a number is a number squaring which gives the original number.
- It is that factor of the number that, when squared, gives the original number.
- It is the value of the power 1/2 of that number.
- The square root of a number is represented as √.
The formula to find the square root is
\sqrt{y} = x \quad \text{if} \quad x^2 = y
**Example: **Square root of 9
⇒ √9 = ± 3
Here, 32 = 9
(-3)2 = 9
The number inside the square root is called the radicand, and the square root symbol is called the radical.
Various other square root formulas are:
- **√x = x 1/2
- **√x . √x = x
- **x√y . x√y = x 2 y
- **√(x × y) = √x × √y
- **√(x / y) = √x / √y
- **x / √y = (x / √y) × ( √y / √y) = (x . √y)/y
- **x / (y + z. √p) = [x / (y + z√p)]×[(y - z√p)/ (y - z√p)] = [x(y - z√p)]/[y 2 - z 2 p]
- **x / (y - z. √p) = [x / (y - z√p)]×[(y + z√p)/ (y + z√p)] = [x(y + z√p)]/[y 2 - z 2 p]