Question

List of first 12 perfect squares:
I.
II.
III.
IV.
V.
VI.
VII.
VIII.
IX.
X.
XI.
XII.
True or False: Lynn said that all square roots are irrational numbers.
Explain your answer and give examples.

Answer 1

### List of the First 12 Perfect Squares:

I. 1
II. 4
III. 9
IV. 16
V. 25
VI. 36
VII. 49
VIII. 64
IX. 81
X. 100
XI. 121
XII. 144

### True or False:
**False**

### Explanation:
Lynn's statement that "all square roots are irrational numbers" is incorrect. While it is true that some square roots are irrational, not all of them are.

Perfect squares, which are the squares of whole numbers, have rational square roots. Here are some examples:

- The square root of 1 is 1 (rational).
- The square root of 4 is 2 (rational).
- The square root of 9 is 3 (rational).
- The square root of 16 is 4 (rational).
- The square root of 25 is 5 (rational).
- The square root of 36 is 6 (rational).
- The square root of 49 is 7 (rational).
- The square root of 64 is 8 (rational).
- The square root of 81 is 9 (rational).
- The square root of 100 is 10 (rational).
- The square root of 121 is 11 (rational).
- The square root of 144 is 12 (rational).

In contrast, square roots of non-perfect squares are irrational numbers. For instance:

- The square root of 2 is approximately 1.414 (irrational).
- The square root of 3 is approximately 1.732 (irrational).
- The square root of 5 is approximately 2.236 (irrational).

Thus, the statement is false because not all square roots are irrational; many square roots of perfect squares are indeed rational.