Behaviour of square roots and Algebraic terms

Today I have got to share a very interesting topic i.e. Square Root in which most of the students or the beginners found difficulties and bit confusion also,

so I’ve thought to explain this

Behaviour of square roots algebraic Terms

But later on I’ve extended this topic towards algebraic terms also, now our topic of discussion today is

How Square Roots behaves:-

so, firstly I want to figure out where the learners found difficulties or what are the key areas where we should keep a keen eye for right solutions.
If I talk about square roots then their behaviour as similar as algebraic Terms behaves i.e.

for same variable:-

x + x = 2x            √2 + √2 = 2√2

x – x  = 0              √2 – √2 = 0

x × x = x²            ( √2 )² = 2

x ÷ x = 1              √2 ÷ √2 = 1

for different variable:-

x+ y = x + y          √2 + √3 = √2 + √3

x – y = x – y           √2 – √3  = √2 – √3

[can be solved further by evaluating square roots]

x × y = xy              √2 × √3 = √ 2×3 = √6

x ÷ y = x/y            √2÷ √3  = √2 / √3

So, I hope you all have cleared your doubted regarding solutions of Square Root.

Q.  but what if square roots and cube roots given

Ans. they will remain unsolved

√2 + ³√2

but to some extent this can be solved like

√2 × ³√2  = (2) raise to the power 5/6

but it will have no impact in subject to solution.
for exponents solutions refer to our post  exponents and their rules