Understanding Square Roots
The square root of a number n is a value that, when multiplied by itself, gives n. It is denoted as sqrt(n) or n1/2. For example, sqrt(25) = 5 because 5 x 5 = 25.
Types of Square Roots
Perfect Squares
Numbers whose square root is a whole number: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100...
sqrt(49) = 7
Simplified Radicals
Irrational roots simplified by factoring out perfect square factors.
sqrt(72) = 6 sqrt(2)
Negative Numbers
Square roots of negative numbers produce imaginary numbers using i = sqrt(-1).
sqrt(-4) = 2i
How to Simplify Square Roots
- Factor the number under the radical into its prime factors.
- Pair up identical prime factors.
- Move each pair outside the radical as a single factor.
- Multiply the factors outside and leave remaining factors inside.
Common Square Root Values
- sqrt(2) = 1.41421...
- sqrt(3) = 1.73205...
- sqrt(5) = 2.23607...
- sqrt(10) = 3.16228...