Question

Between what two integers does √98 lie?

Answer 1

one way is this:

if the 2 integers are x and y, then

x<√98<y

if we assume that x and y aer both positive then

square everybody

x²<98<y²

solve each

x²<98

square root both sides

x<9.89

since x must be an integer, x=9

98<y²

squaer root both side

9.89<y

since y must be an integer, y=10

√98 lies between 9 an 10

Answer 2

Which perfect square is less than 98?  More than 98?

9^2 = 81, and 10^2 = 100.

Since 81 < 98 < 100,

√81 < √98 < √100.

Therefore, 9 < √98 < 10∫

√98 lies between the integers 9 and 10.