To find the greatest value

gmattesttaker2 wrote:
Which of the following is greatest?
(A) 6√7
(B) 9√4
(C) 7√6
(D) 6√8
(E) 8√5

One option is to take the integers in front of the roots and rewrite them as roots.
Then we'll use the fact that (√x)(√y)= √(xy)
I'll also use some general estimation. For example, (36)(7) is less than (40)(7) [aka 280]
So, √(36)(7) = √(some number less than 280)
Likewise, (81)(4) is greater than (80)(4) [aka 320]
So, √(81)(4) = √(some number greater than 320)
That's as precise as we need to be here.


Here's what I mean:
(A) 6√7 = (√36)(√7) = √(some number less than 280)
(B) 9√4 = (√81)(√4) = √(some number greater than 320)
(C) 7√6 = (√49)(√6) = √(some number less than 300)
(D) 6√8 = (√36)(√8) = √(some number less than 320)
(E) 8√5 = (√64)(√5) = √(320)

So, B must be the greatest

Cheers,
Brent