1 Crore+ students have signed up on EduRev. Have you? 
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:
33 videos34 docs140 tests

Use Code STAYHOME200 and get INR 200 additional OFF

Use Coupon Code 
33 videos34 docs140 tests
