Types of Algebraic Expressions 4 + √
__ 2
1 √
___ √
__ 2
______ √
__ 3
______ √
__ 2 + 1
__ 3
√ =
= 1 ___
__ 2
=
_______ √
(4 + √ × √
_______ √
( √
__ 2 + 1)
__ 2
___ √
__ 2
__ 3
__ 2
__ 3 )
= √ × √
___ 2
__ 2
___ √
__ 2
__ 2
× √
___ √
__ 3
__ 3
= 4 √
________ 2
__ 2 + √
__ 6
4 = √
_______ 3
__ 6 + √
__ 3
1. Write the following in their simplest form: (a) √ (b) √ (c) √ (d) √ (e) √ (f) √ (g) √ (h) √ (i) √
___ 12
___ 27
___ 50
___ 45
___ 75
___ 32
___ 98
___ 72
___ 11 − 2 √
___ 28 + √
__ 8 + √
__ 2 × √
__ 2 ) 3
__ 6 (3 √
_____ 1210
(j) √ (k) √ √
(l)
(m) √ (n) √ (o) √
2. Simplify the following: (a) √
(b) 5 + 7 √ (c) x + √ (d) √ (e) √ (f) √ (g) √
__ y − 3 √
____ 125 − 2 √
___ 75 − 3 √
(c) 2 √ (d) √
(e) ( √ (f) ( √
__ 6 × 5 √
__ 3
__ 3 − 9 + 8 √
___ 63 − √
___ 12 + √
___ 11 + 4 √
__ y + 2x − 5 √
__ 3
____ 180 + √
___ 48 + √
____ 175
___ 18 + √
____ 147
____ 245
___ 27
3. Multiply out and simplify the following: (a) ( √ (b) √
__ 3 + 1 ) 2
__ 2 + 2 √
___ 18
__ 3 − 1)( √
__ 3 + √
__ 3 + 1)
__ 6 )
___ 11
__ y
____ 512
__ 8
___ 18
__ 9
____ 108
___ 25
____ 36
____ 147
____ 100
___ 75
___ 36
EXERCISE 7 (g) √ (h) ( √ (i) ( √
___ ab (a √
__ 7 + √
__ 7 + √
___ √
__ 5
√
__ 3
__ b + b √
___ 13 ) 2
___ 13 )( √
__ a )
__ 7 − √
___ 13 )
4. Rationalise the denominator in the following: (a) 1
(e) −3 ____
2 √
(b) − 1 ___
√
(c) 2 ___
(d) 4
____ 5 √
__ 2
5. If x = √ fi nd x 2 + xy + y 2.
__ 3 + √
__ 2
(f) √ (g) x
(h) √
__ 2 and y = √
____ 2 √
__ 6
___ √
__ y
__ 3 − √
___ √
__ x
__ y
__ 2 ,
6. In a random sample of 1000 Irishmen, 560 were married.
The confi dence interval for a population proportion at the 95% signifi cance level is
given by (
___ √
__ n ,
p − 1 ___
__ n
√ ) % − ( (c) p – 1
___ √
__ n
(d) p + 1
___ √
__ n
, .
p + 1 ___
__ n
√ ) %, where p is
the percentage of married men in the sample and n is the size of the sample.
Find, correct to two decimal places: (a) p, (b) 1
__ 7
__ 3
85
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