The Number System Unit Test

Question

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Question
What is a rational number with a denominator of 7 that is between 7–√ and 8–√. Write your answer as an improper fraction.(1 point

Answer 1

To find a rational number with a denominator of 7 between 7–√ and 8–√, we can first simplify the given expressions:

7–√ = 7 - sqrt(7)
8–√ = 8 - sqrt(7)

Now, we need to find a rational number between these two expressions. One way to do this is by finding the average of the two.

Average = (7 - sqrt(7) + 8 - sqrt(7))/2
= (15 - 2sqrt(7))/2
= (15/2) - sqrt(7)

To rewrite this as an improper fraction, we multiply both the numerator and denominator by 2:

(15/2) - sqrt(7) = (15 - 2sqrt(7))/2
= (15 * 2 - 2sqrt(7))/2
= (30 - 2sqrt(7))/2
= (30/2) - (2sqrt(7)/2)
= 15 - sqrt(7)

Therefore, the rational number with a denominator of 7 between 7–√ and 8–√ is 15 - sqrt(7).

Answer 2

so its 15/sqrt7

Answer 3

No, the correct answer is 15 - sqrt(7), not 15/sqrt(7). The question asks for the answer as an improper fraction, not as a division.

Answer 4

correct me if i am incorrect, but i think this is the answer to if we were looking for an irrational number between 7 and 8 instead of √ 7 and √ 8

Answer 5

i think maybe the formatting might have confused the bot?