Answer:
a) 23 and 24
b) see step-by-step
c) 23.2
Explanation:
a) find the greatest square number below 540?
find the smallest square number above 540?
23² = 529 and 24² = 576
529 < 540 < 576
⇒ √529 < √540 < √576
⇒ 23 < √540 < 24
Hence, √540 lies between 23 and 24
b) **I'm not sure how accurate they want this, so I've added several options**
√540 = 23.23790008...
23.23790008... - 23 = 0.2379000772...
0.2379000772... = 2,379,000,772 / 10,000,000,000
Therefore, √540 = 23 and 2,379,000,772 / 10,000,000,000
Or 23 and 2,379 / 10,000
Or 23 and 24/100 = 23 and 6/25
Or 23 and 2/10 = 23 and 1/5
c) (√540)² = 540
So we are looking for a number whose square is 540.
We know that √540 lies between 23 and 24 (from part a), so let's start with 23.5:
23.5² = 552.25
552.25 > 540 so try a smaller number
23.3² = 542.89
542.89 > 540 so try a smaller number
23.2² = 538.24
538.24 < 540
23.24² = 540.0976
540.0976 > 540
So √540 lies between 23.2 and 23.24, therefore, the decimal approximation is 23.2 to the nearest tenth place