You must be having a good understanding of concepts of surds and indices to solve the problems faster in CAT ..
http://catdumps.blogspot.com/2009/03/cat-gmat-gre-mba-index-if-m-is-positive.html
Here are the Laws of SURDS AND INDICES
http://catdumps.blogspot.com/2009/03/laws-of-surds-and-indices.html
Multiplying and Dividing
To multiply powers with the same base, keep the same base and add the exponents
3 5 3+5 8
b X b = b = b
To divide powers with the same base, keep the same base and subtract the exponents
10 8 10-8 2
b / b = b = b
Raised Powers to Powers
To raise a power to a power, multiply the exponents:
3 5 3x5 15
(b ) = b = b
Negative Powers
A number raised to a negative exponent is simply the reciprocal of that number raised to the corresponding positive exponent.
-3
2 = 1 / 2^3 = 1 /8
Simplifying Roots
To simplify a square root, factor out the perfect squares under the radical, remove the perfect squares and put the result in front:
__ ____ __ __ __
V20 = V4X5 = V4 X V5 = 2 V5
Adding and Subtracting Roots
You can add or subtract radical expressions when the part under the radicals is the same
__ __ __
2 V6 + 3 V6 = 5 V6
Don't try to add or subtract when the radicals are different.
You cannot simplify expressions like:
___ __ ___ ___
2 V 5 + 3 V 6 {is not equal to 5V 6 or 5V 6 }
Multiplying and Dividing Roots
The product of square roots is equal to the square root of the product:
__ __ ______ __
V 5 x V3 = V5 X 3 = V15
The quotient of square roots is equal to the square root of the quotient:
__ __ ____ ___
V8 /V2 = V8/2 = V 4 =2