Definition
Root is the inverse of exponent. For example;- 42 = 16, so 16 = 4
- 52 = 25, so 25 = 5
- 102 = 100, so 100 = 10
Simplifying Square Roots
You can simplify a root by factoring the root number another number that is rational. Or in other words, divide the root number by the perfect squares. For example;-
Simplify 60
60 = 4 × 15 = 215
-
Simplify 48
48 = 16 × 3 = 43
-
Simplify 125
125 = 25 × 5 = 55
Root Operations
Addition
Roots with coefficient can be added with another coefficient that have the same roots.ac + bc = (a + b)c
- 32 + 42 = (3 + 4)2 = 72
- 5 + 35 = (1 + 3)5 = 45
Subtraction
Roots with coefficient can be subtracted with another coefficient that have the same roots.ac - bc = (a - b)c
- 73 - 43 = (7 - 4)3 = 32
- 106 - 56 = (10 - 5)6 = 56
Multiplication
Roots can be multiplied with any other roots. If the root is the same as the other multiplied root, the root can be deleted (if you want to be faster).ac × bd = (a × b)c × d
- 2 × 5 = 10
- 32 × 43 = (3 × 4)2 × 3 = 126
- 25 × 35 = (2 × 3)(5) = 6(5) = 30
Division
Roots can be divided with any other roots.ac ÷ bd = (a ÷ b)c ÷ d
- 86 ÷ 43 = (8 ÷ 4)6 ÷ 3 = 22
Rationalising Roots
We can rationalise or simplify a fraction with a root denominator. To rationalise a root, multiply the fraction with a fraction of opposite roots. For example:
Example 1:
Example 2:
Example 3: