Question

Examine each number. What number can you add to this number to make a number that has a whole-number square root?

a) 42 c) 470
b) 101 d) 1000

Answer 1

9514 1404 393

Answer:

a) 7

b) 20

c) 14

d) 24

Explanation:

The desired number is found by subtracting the given number from the square of the integer just higher than the root of the given number.

a) √42 ≈ 6.5, so the desired number is 7² -42 = 49 -42 = 7

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b) √101 ≈ 10.05, so the desired number is 11² -101 = 121 -101 = 20

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c) √470 ≈ 21.7, so the desired number is 22² -470 = 484 -470 = 14

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d) √1000 ≈ 31.6, so the desired number is 32² -1000 = 1024 -1000 = 24