What are Surds?
The roots of those quantities which cannot be exactly obtained are called Surds.
Examples: √3, 2√5, 7√2
What are Indices?
The expression 25 is defined as follows:
2^{5} = 2 × 2 × 2 × 2 × 2
We call "2" the base and "5" the index.
Shortcut to Remember Surds & Indices:
1. If √(X/0.0081) = ∛0.009 , the value of x is:
a) 0.729
b) 0.0729
c) 0.000729
d) 0.00729
e) None of these
√(X/0.0081) = ∛0.009
Or, √x/0.09 = ∛(9/1000)
Or, √x = 0.09 × 3/10
Or, √x = 0.027
Or, x = (0.027)2 = 0.000729
So, answer is option c.
2. The value of √(9+ √(604+ √(424+ √(273+ √256) ) ) ) = ?
a) 8
b) 6
c) 5
d) 7
e) None of these
√(11+ √(604+ √(424+ √(273+ √256) ) ) )
= √(11+ √(604+ √(424+ √(273+ 16)) ) )
= √(11+ √(604+ √(424+ √289) ) )
= √(11+ √(604+ √(424+ 17)) )
= √(11+ √(604+ √441) )
= √(11+ √(604+ 21))
= √(11+ √625)
= √(11+ 25)
= √(11+ 25)
= √36
= 6
So, answer is option b.
3. Simplification: 25^{2.7} × 5^{4.2} ÷ 5^{5.4} = ?
(625)^{0.16} × (625)^{0.09}
= (625)^{0.16 + 0.09}
= (625)^{0.25}
= (625)^{1/4}
= 5^{4 × ¼}
= 5
So, answer is option e.
1. Laws of Indices:
2. Surds:
Let a be rational number and n be a positive integer such that a^{(1/n)} =
Then, a is called a surd of order n.
3. Laws of Surds:
37 videos53 docs148 tests

1. What is a surd? 
2. What is an index in surds and indices? 
3. How do you simplify surds? 
4. What are the operations performed on surds? 
5. How do you solve equations involving surds and indices? 
37 videos53 docs148 tests


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