Question

If x=6, what is the smallest natural number y that makes x2+y2 rational?

Answer 1

Given: If x=6, what is the smallest natural number y that makes x2+y2 rational .

To Find: Smallest value if y so that the expression is rational .

Solution : On substituting x = 6 , we have

$=> x^2+y^2= 6^2+y^2\\\\ x^2+y^2= 36+y^2$

Now for the whole expression has minimum value y^2 should be minimum , also y should be natural no. The set of Natural no. is ,

$=> N=\{ 1,2,3,4,... ..,\infty\}$

Therefore the smallest Natural no. is 1 . Therefore minimum value of y is 1.

The minimum value of y is 1.