Question

If a is an integer, which of the 

following could be a4 ?
A. 1.6 X 10^11
B. 1.6 X 10^12
C. 1.6 X 10^13 
D. 1.6 X 10^14
E. 1.6 X 10^15

Answer 1

So to work this out we need to find the 4th root of each of those and pick the one that gives an integer.

A:
`\sqrt[4]{1.6*10^1^1} = 632.455...` This is a decimal therefore not an integer.

B:
`\sqrt[4]{1.6*10^1^2} =1124.682...` Again a decimal, therefore not an integer.

C:
`\sqrt[4]{1.6*10^1^3} =2000` This is a whole number, so it is an integer.

D:
`\sqrt[4]{1.6*10^1^4} =3556.558...` Decimal, therefore not an integer

E:
`\sqrt[4]{1.6*10^1^5} =6324.555...` Again a decimal, not an integer.

The only one that gives an integer when put to the 4th root is C, therefore:


`1.6*10^1^3` could be A^4, as the 4th root of it is an integer.