Chapter 2. Exponents and Radicals

MODULE - 1
Algebra
Exponents and Radicals
Notes
2 +
3. Simplify:
2 −
3 2 −
+
3 2 +
4. Rationalise the denominator of
5. If a = 3+ 2 2 . Find a + 1 .
a
3
3
1
3 − 2 −1
2 + 5 7
6. If = x + 7 y , find x and y.
2 − 5 7
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LET US SUM UP
• a × a × a × ..... m times = a m is the exponential form, where a is the base and m is the
exponent.
• Laws of exponent are:
m
⎛ a ⎞ a
(i) a m × a n = a m+n (ii) a m ÷ a n = a m–n (iii) (ab) m = a m b m (iv) ⎜ ⎟ =
m
⎝ b ⎠ b
a = a (vi) a o −m
1
= 1 (vii) a =
m
a
(v)
m n mn
( )
p
• q q p
a =
a
• An irrational number n x is called a surd, if x is a rational number and nth root of x is
not a rational number.
• In n x , n is called index and x is called radicand.
• A surd with rational co-efficient (other than 1) is called a mixed surd.
• The order of the surd is the number that indicates the root.
• The order of n x is n
• Laws of radicals (a > 0, b > 0)
n
a
n
= (ii) n n n
n
a × b = ab (iii)
n =
b
(i) [ a ] n
a
a
b
m
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Mathematics Secondary Course