Question

suppose b is a positive integer such that 2⁴ by b² is also an integer. what are the possible values of b?​

Answer 1

2⁴=16

For the ratio $\frac{ {2}^{4} }{ {b}^{2} }$

to be an integer, b⁴<16 and a factor of 16

So, the possible values of b⁴ are 1,2,4,8,16

Hence, possible values for b are $1, \sqrt{2},2, 2 \sqrt{2} ,4$

Answer 2

Answer:Given that

b=+veZ & 2^4/b^2=Z ;then b=?

Step-by-step explanation:

2^4=16

16\b^2=Z

From trail and error method:-

If b=1

16\1^2=16\1 =>16(Integer[Z])

If b=2

16\2^2

=>16\4. [2^2=4]

=4[Z]

If b=3

16\3^2

=>16\9. [3^2=9]

=>1.77777------- (it's not an integer)

So, b is not = to 3

Continue the same process to get more values of "b"....

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