Video: Identifying a Set of Numbers under a Given Condition Involving Exponents

Which of the following sets of numbers has square roots between 7 and 8? [A] 50, 62, 51 [B] 48, 51, 65 [C] 48, 50, 62 [D] 48, 62, 65 [E] 62, 51, 65

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Video Transcript

Which of the following sets of numbers has square roots between seven and eight?

So in order to do this, what numbers have square roots of seven and eight? Well, we can find that out by squaring seven and squaring eight. Seven squared is equal to 49 and eight squared is equal to 64. Let’s go ahead and place these on our number line.

So if we were to place seven here and eight here, a seven squared is 49, then we can also represent seven as a square root of 49. And then for eight, we could represent it as a square of 64. So it says, which of the following sets of numbers has square roots between seven and eight? So we want a set of numbers that are between 49 and 64. So our numbers could be 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, or 64. And technically, if they need to be between seven and eight, it will be greater than 49 and less than 64.

So option A 50, 62, and 51: all three of those numbers are between 49 and 64. So let’s check B 48, 51, 65: 48 is less than 49 and 65 is greater than 64. So we can eliminate option B. Option C also has 48 even though 50 and 62 both work. So we still have to eliminate option C. Now for D, 48 is two small and 65 is too large. So we can eliminate option D. And then for option E, 65 is too large. So option E is not an option for our final answer.

So the square root of 50 would land here, the square root of 62 would be around here, and the square root of 51 would be around here.

Therefore, the set of numbers that has square roots between seven and eight will be 50, 62, and 51.

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