Page 107 - Mathematics_Form_Two

Exponents and radicals

1
7. (32) 1
5
1   4  4 1
1
1 (c) 4 16 =      = 2 ,
2
8. (1.21)   
2
1 is the fourth root of 1 .
1 2 16
9. æ 27 ö 3
FOR ONLINE READING ONLY
ç ÷
è 64 ø Note that, the square root of a negative
1 7 real number does not exist in the set of
real numbers.
10. (3 ) .(3 )x 3 x 3
2
(3 ) x 3 Example 5�25 Mathematics for Secondary Schools
1
1
1
1
11. (c d )(c −d ) Find the square root of 196.
2
2
2
2
Solution
1 ⎛ 1 ⎞ Factorize 196 in terms of prime factors:
2⎟
2 ⎜
12. (2y) + z ) (2y) −z ⎟ ⎟ ⎟ ⎟ ⎠ 196 = 2 × 2 × 7 × 7
⎜
2
2
⎜
⎜
⎝
2
2
= 2 × 7
2
2
1
13. 3(5) +7(5) 1 2 So, 196 = 2 × 7 .
2
Apply the radical sign in both sides of
14. 1 1 the equation and simplify to obtain,
10(3) −4(3) 3
3
2
196 = 2 ´ 7 2
1
1
15. 2+2(2) +(8) +3(2) 1 2
2
2
2
= 2 × 7 2
1
( ) ( ) 1 2
2
´
7
2
=
2
2
Radicals 1
n
A rational exponent, x which can be 27= ´
14=
expressed as n x is known as a radical.
In x n is an index, is the radical Therefore, 196 14= .
,
n
symbol and x is the radicand. The symbol Example 5�26
is also called a surd.
Find the cube root of 216.
The expression x is also known as the Solution
n
n root of x, which is a number that, when Write 216 as a product of prime factors:
th
multiplied n times, gives the original 216 = 2 × 2 × 2 × 3 × 3 × 3 = 2 × 3 3
3
number x. For example:
Apply the cube root on both side, to obtain
1 1 3 3 3 3
2
(a) 4 = (4) = ( ) = 2 216 = 2 3´
2
2
2
3
3
3
2 is the square root of 4. = 2 × 3 3
1 1
2
1 1 = ( ) (3 3 3 ´ 3 3 )
3
3
(b) 343 = (343) = ( ) = 7 = 2 × 3 = 6
7
3
3
7 is the cube root of 343. Therefore, the cube root of 216 is 6.
101
Student's Book Form Two
11/10/2024 20:12:25
MATHEMATIC F2 v5.indd 101
MATHEMATIC F2 v5.indd 101 11/10/2024 20:12:25