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 -

Al Azhar 9th Grade Lesson Notes

Table of Contents

Root