math hl question

[srishti]

find the square root of
9+2√18

without the calculator and with proper steps.
you can copy the root sign from here :√

 

[celoth]

1st,
you hafta start with this model:
(√a+√b)^2 = a+b+2√(ab)

sqrt of a+b+2√(ab) = √a+√b
sqrt of 9+2√18 = ?

by comparing the above 2 :
sqrt of 9+2√18 = sqrt of 3+6+2√(3x6)
where a=3, b=6 or vice versa,

sqrt of 9+2√18 = √3+√6