Are these rational numbers?

Question

1.Square root of 121

2.Square root of 200

Note: Some people refer to square root as a rad. So rad 121 and rad 200.

I need to determine if either number is natural, whole, an integer, rational, or irrational numbers.

This question is simple enough, but I'm asking because my textbook says.

"If a positive rational number is not a perfect square such as 25 or 4/9, then its square root is irrational."

It confused me as 25 is a perfect square. (5x5=25).

-Thanks in advance for any help.

Answer 1

121 = 11*11 so sqrt(121) is a natural number, whole number, an integer and a rational number.

200 = 100 * 2

100 = 10*10

so sqrt(200) = sqrt(100*2) = sqrt(100)*sqrt(2) = 10*sqrt(2)

so sqrt(200) is an irrational number because 2 is not a perfect square

Answer 2

√ 121 = can equal -11 or +11

natural starts at 1 so -11 is not natural , but is an integer, rational and real

+11 is natural ,whole, is an integer, rational and real

√200  = √100 * √2  = 10√2 =  irrational and real

Answer 3

1.rational whole integer

2.irrational #

Answer 4

1. is, the square root of 121 is 11

2. isn't, the square root of 200 is 10*√2

Edit: You're misreading the line in the book, it's giving 25 and 4/9 as examples of numbers that are perfect squares, if there was a comma after perfect square, they would be examples of non-perfect squares. It's poorly worded; it's not really your fault.

Edit: #1 and #2 should be ±11 and ±10*√2 , but that wasn't your real question anyway.

Answer 5

sqrt of 121 is 11.

sqrt of 200 is irrational.