estimating the square root

87 = 81 + 6

you can approximate sqrt 87 by taking
sqrt 81 = 9
sqrt 100 = 10

and use linear interpolation

I don't understand why estimating the square root of 87 gives an answer of 9.3 ?

What was the original question?

estimate the square root of 87

there is a 9 and 3 because the answer is 9.3

sqrt 81 = 9, sqrt 100 = 10
to go from 81 to 100, there are 19 "steps"
so 19 "steps" = 10 - 9 = 1
to approximate sqrt 87, we need to go 6 "steps" from 81
so the answer is ?

What level of maths e.g. GCSE/A Level? Where was this question - in a textbook/exam paper? If it was a textbook/worksheet, was it part of a larger topic?

Without context, the question can be answered in a variety of ways and there's no way of knowing how precise you need to be.

GCSE edexcel maths higher level textbook
estimating square roots

use iteration.

N(x_0) = (1/2)(guess+ (87/guess))
N(x_1) = (1/2)(previous answer+ (87/previous answer))
and so on.

this would be a non-calculator question

So make your first guess 10