   SEARCH HOME Math Central Quandaries & Queries  Question from Dorothy, a parent: 1. Explain why the number 123, 456, 789, 101, 112 cannot be a perfect square. (Hint: What is the units digit?) 2. A substance doubles in volume every minute. At 9:00A.M., a small amount is placed in a container. At 10:00A.M., the container is just full. At what time was the container one-eighth full? Dorothy,

1. Explain why the number 123, 456, 789, 101, 112 cannot be a perfect square. (Hint: What is the units digit?)

If a number ends in 0, what does its square end in? Is this always true?
If a number ends in 1, what does its square end in? Is this always true?
If a number ends in 2, what does its square end in? Is this always true?

Complete the pattern.

1. A substance doubles in volume every minute. At 9:00A.M., a small amount is placed in a container. At 10:00A.M., the container is just full. At what time was the container one-eighth full?

Try with some easier numbers (eg, it takes three minutes, four minutes, five minutes, or six minutes,to fill the container.) Make a conjecture and test it with another number.

Good Hunting!
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