Which placement of grouping symbols in the expression gives it a value of 22?

3 • 4 – 2 + 5 +7

a.
3 • [4 – (2 + 5) + 7]

b.
(3 • 4) – [2 + (5 + 7)]

c.
[(3 • 4) – 2] + (5 + 7)

d.
3 • (4 – 2) + (5 + 7)

9514 1404 393

  a) 22

  b) 18

Step-by-step explanation:

a) In order for 198k to be a perfect square, all of its integer factors must be squares. 3² is already a factor. To make the other factors be squares, need to multiply by 2 and 11. That is, k = 2×11 = 22. Then we will have ...

  198k = 2×3²×11 × (2×11) = 2²×3²×11² = (2×3×11)²

  k = 22

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b) The factors that are different in the two numbers are 11 and 5. The factors that are the same are 2×3² = 18.

  18 is the greatest common factor of 198 and 90

The "work" is looking at the numbers in the factor lists and comparing those to what is needed to answer the question.