K T.

asked • 08/17/21

(5+3√2)^2=p+q/√8, where p and q are integers. Find the value of q.

(5+3√2)^2=p+q/√8, where p and q are integers. Find the value of q. I'm not sure what to do.

1 Expert Answer

By:

Yefim S. answered • 08/17/21

Tutor
5 (20)

Math Tutor with Experience

See tutors like this
See tutors like this

(5+3√2)2 = 25 + 30√2 + 18 = 43 + 60/√2 = 43 + 120/√8 = p + q/√8. From here p = 43 and q = 120

Upvote • 1 Downvote
More
Report

K T.

how did you get 43+60/√2? I got 43+30√2.
Report

08/17/21

Zachary M.

Hello K.T. when I answered this question I first expanded (5+3sqrt(2))^2 to get 43+30sqrt(2). Then I multiplied both sides of the equation by sqrt(8) and simplified to get p+q= 86sqrt(2) +120. So p=86sqrt(2) and q=120. However this doesn't make sense since both p and q should be integer values and p is an irrational number. However, q is indeed an integer and the answer is 120. Just to clarify, is it (p+q)/sqrt(8) or p+q/sqrt(8)? If it is the latter, the answer that Yefim provided would be right since 60/sqrt(2) is equal to 30sqrt(2) when you rationalize the denominator. You can then get the denominator to be sqrt(8) by setting up a proportion and then it will expose the answer of 120. Note that 30*sqrt(2)= 60/sqrt(2)= 120/sqrt(8).
Report

08/19/21

Still looking for help? Get the right answer, fast.

Ask a question for free

Get a free answer to a quick problem.
Most questions answered within 4 hours.

OR

Find an Online Tutor Now

Choose an expert and meet online. No packages or subscriptions, pay only for the time you need.