Square Roots (√x) and Cube Roots (∛x)

This is our first post on Upavidhi Blog, and we decided to discuss polynomials - especially because polynomials are an intrinsic part of mathematics. From the first time that we learn what an equation is, to calculus, to numerical analysis to advanced mathematics - there is no other concept that finds such abundant usage in mathematics.
 
This is one of the many areas where knowledge of Vedic Mathematics can be effectively applied. Moreso because, it simplifies most of its basic operations - allowing oneself to concentrate on the overall mathematical problem, rather than getting entangled in the cumbrous poly-operations.
 
SQUARE ROOT (√x) OF A NUMBER:

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Let us refresh our memories, ...
Works only on perfect squares. Unreliable, and used in Vedic Mathematics to prove the mathematical derivation.
 
CUBE ROOT (∛x) OF A NUMBER:

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Let us refresh our memories, ...
Works only on perfect cubes. Unreliable, and used in Vedic Mathematics to prove the mathematical derivation.
 
MISCELLANEOUS NOTES:

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It should be noted that polynomials with more than one indeterminate (variable) tend to get tricky, and Vedic Mathematics should only be applied after much practice. For example:  
To conclude, knowledge of Vedic Mathematics indeed works wonders - especially in speeding up the operations, eradicating chances of silly mistakes, and most importantly, in helping one to visualize the entire process in a simple, transparent manner. These advantages, in turn, allows oneself to concentrate on the overall mathematical problem.
 
However, in line with our stand at Upavidhi, it should only be viewed as an extension to the conventional methods, and applied only after expertise - that comes though practice, and a certain amount of mathematical skill.