Question

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Answer 1

Answer:

a) 23 and 24

b) see step-by-step

c) 23.2

Step-by-step 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