Simplify Surds
√(ab) = √a√b
NUMERIC EXAMPLE
√(16 × 9) = √16√9= 4 × 3 = 12
√(16 × 9) = √(144) = 12
Using √(ab) = √a√b
EXAMPLE
√12 = √(4 × 3) = √4√3= 2√3
LEVEL 1
FIRST
Find the square number
SECOND
Express the surd as a product of the square number and another number
THERE IS LESS CHANCE OF ERROR IF YOU WRITE THE SQUARE NUMBER
BEFORE THE OTHER NUMBER
Example 1
√12 square number is 4
= √(4 × 3)
= √4√3 USE THIS STEP TO AVOID ERROR= 2√3
Example 2
√50 square number is 25
= √(25 × 2)
= √25√2
= 5√2
Example 3
√80 square number is 16
= √(16 × 5)
= √16√5
= 4√5
LEVEL 2
FIRST
Find the square number
SECOND
Express the surd as a product of the square number and another number
THERE IS LESS CHANCE OF ERROR IF YOU WRITE THE SQUARE NUMBER
BEFORE THE OTHER NUMBER
Example 1
3√20 square number is 4
= 3√(4 × 5)
= 3√4√5
= 3 × 2√5 USE MULTIPLICATION SIGN TO AVOID ERROR
= 6√5
Example 2
2√300 square number is 100
= 2√(100 × 3)
= 2√100√3
= 2 × 10√3
= 20√3
Example 3
5√72 square number is 36
= 5√(36 × 2)
= 5√36√2
= 5 × 6√2
= 30√2
LEVEL 3
FIRST
Find the square number for each surd
SECOND
Express each surd as a product of the square number and another number
THERE IS LESS CHANCE OF ERROR IF YOU WRITE THE SQUARE NUMBER
BEFORE THE OTHER NUMBER
Example 1
√72 + √12 square numbers are 36 and 4
= √(36 × 2) + √(4 × 3)
= √36√2 + √4√3
= 6√2 + 2√3
Example 2
√40 - √32 square numbers are 4 and 16
= √(4 × 10) - √(16 × 2)
= √4√10 - √16√2
= 2√10 - 4√2
Example 3
- √8 + √20 square numbers are 4 and 4
= - √(4 × 2) + √(4 × 5)
= - √4√2 + √4√5
= - 2√2 + 2√5
= 2√5 - 2√2
LEVEL 4
FIRST
Find the square number for each surd
SECOND
Express each surd as a product of the square number and another number
THERE IS LESS CHANCE OF ERROR IF YOU WRITE THE SQUARE NUMBER
BEFORE THE OTHER NUMBER
Example 1
2√72 + √32 square numbers are 36 and 16
= 2√(36 × 2) + √(16 × 2)
= 2√36√2 + √16√2
= 2 × 6√2 + 4√2
= 12√2 + 4√2
= 16√2
Example 2
√40 - 5√32 square numbers are 4 and 16
= √(4 × 10) - 5√(16 × 2)
= √4√10 - 5√16√2
= 2√10 - 5 × 4√2
= 2√10 - 20√2
Example 3
- 14√8 + 7√20 square numbers are 4 and 4
= - 14√(4 × 2) + 7√(4 × 5)
= - 14√4√2 + 7√4√5
= - 14 × 2√2 + 7 × 2√5
= - 28√2 + 14√5
= 14√5 - 28√2
LEVEL 5
FIRST
Find the square number for each surd
SECOND
Express each surd as a product of the square number and another number
THERE IS LESS CHANCE OF ERROR IF YOU WRITE THE SQUARE NUMBER
BEFORE THE OTHER NUMBER
Example 1
√72 + √48 + √27
square numbers are 36, 16 and 9
= √(36 × 2) + √(16 × 3) + √(9 × 3)
= √36√2 + √16√3 + √9√3
= 6√2 + 4√3 + 3√3
= 6√2 + 7√3
Example 2
2√72 + 3√48 + 4√27
square numbers are 36, 16 and 9
= 2√(36 × 2) + 3√(16 × 3) + 4√(9 × 3)
= 2√36√2 + 3√16√3 + 4√9√3
= 2 × 6√2 + 3 × 4√3 + 4 × 3√3
= 12√2 + 12√3 + 12√3
= 12√2 + 24√3
Example 3
- 2√72 + 3√48 - 4√27
square numbers are 36, 16 and 9
= - 2√(36 × 2) + 3√(16 × 3) - 4√(9 × 3)
= - 2√36√2 + 3√16√3 - 4√9√3
= - 2 × 6√2 + 3 × 4√3 - 4 × 3√3
= -12√2 + 12√3 - 12√3
= -12√2
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