Power of Maths: Paper 1 – Section 2
ACTION ACTIVITY
ACTION Simplifying surds
OBJECTIVE To break surds down into their simplest form
ACTIVITY ACTION CTION Adding surds
OBJECTIVE To combine surds into their simplest form
Y 26 Y 25
Adding and subtracting surds As usual, you can only add and subtract like terms. You cannot simplify √ but 2 √
__ 2 + 5 √
3 + √ 2 √
= 2 √ = 2 √ = 2 √ = − √
__ 5 + √
__ 5 + 6 − 2 √
__ 5 + √
__ 5 + 3 √
__ 5 + 3 √
__ 5
__ 2 + 7 √
___ 45 − 3 √
__ 5 + 5 √
_____ 9 × 5 − 3 √
___ 20
__ 5 − 6 √
__ 5
__ 5 − 3 × 2 √
__ 2 = 14 √
__ 2 + √
__ 3 into a single surd,
__ 5 = 9 + 4 √
_____ 4 × 5
__ 5
__ 5
__ 2 . [Just as 2a + 5a + 7a = 14a.]
Multiplication of surds ACTIVITY ACTION CTION Multiplying surds
OBJECTIVE To multiply surds and to break them down to their simplest form
Y 27
To multiply out brackets with surds, multiply each term in one bracket by each term in the other bracket and combine like terms. Remember: √
2( √
__ 3 + 4 √
(3 + √ ( √
__ 2 )(4 − 5 √
= 12 − 11 √ = 2 − 11 √
__ 3 + √
(3 √
= 3 + 2 √ = 5 + 2 √
__ 2 ) 2 = ( √
__ 2
__ 6 + 2
__ 2 − 5)(3 √
__ 2 ) = 2 √
__ a × √
__ b = a
__ 2 − 10
__ 2
1
__ 2 ) = 12 − 15 √
__ 3 + 8 √
__ 2
__ 3 ) 2 + 2( √
__ 3 )( √
__ 6 [Perfect square]
__ 2 + 5) = (3 √
× b = (ab) = √
__ 2
1
__ 2
1
__ 2 + 4 √
___ ab
__ 2 − 5 √
__ 2 ) + ( √
__ 2 ) 2
__ 2 ) 2 − (5 ) 2 = 9 × 2 − 25
= 18 − 25 = −7 [Difference of two squares] ACTIVITY ACTION CTION
Rationalising the denominators of surds
OBJECTIVE To rationalise by multiplying above and below by a surd
Y 28 Division (rationalising the denominator)
When you divide surds, the answer should never have a surd in the denominator. This process of getting rid of surds on the bottom is called rationalising the denominator. 3
___ √
__ 2
= 3 ___
√ √
___ √
__ 5
__ 7
__ 2
× √ = √
___ √
__ 5
__ 7
___ √
__ 2
__ 2
= 3 √ × √
___ √
__ 7
__ 7
____ 2
__ 2
To rationalise a surd of the form a = √
____ 7
___ 35
___ √
__ b
, multiply above and below by √
__ b .
__ 4 [ √
__ 2 × √
__ 2 = √
__ 4 ]
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