Answer:
(a) 4.2
Explanation:
You want an estimate of √18 to one decimal place.
Square root
The squares on either side of 18 are 4² = 16 and 5² = 25. The value 18 is about (18 -16)/(25 -16) = 2/9 of the way between these numbers. So, an estimate of the square root is ...
4 + 2/9 ≈ 4.2
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Additional comment
A fast way to improve the estimate is to take the average of this value and the quotient of 18 and this value:
(4.2 +18/4.2)/2 ≈ 4.2429
Compare this to the actual root of 4.2426.
Using that same method again gives a value that matches the root when rounded to 8 decimal places.