Perfect Squares

If the square root of a number is an integer, the number is called a perfect square. One example of a perfect square is...

• 50

• 81

The square root of a perfect square is an

• integer

• irrational number

Which of the following lists includes only perfect squares

• 49, 144, 16, 1, 64

• 81, 49, 100, 2, 9

Since 2 is not a perfect square, square root of 2 is not an integer. The square root of 2 is a number which, when squared, equals exactly...

• 4

• 2

Let's try to find the square root of 2. It must be between

• 1 and 2

• 2 and 3

Fact: (1.4)² = 1.96 and (1.5)² = 2.25. Therefore square root of 2 is

• between 1.4 and 1.5

• not between 1.4 and 1.5

Fact: (1.41)² = 1.9881 and (1.42)² = 2.0164. Therefore square root of 2 is

• between 1.41 and 1.42

• not between 1.41 and 1.42

Fact: (1.414)² = 1.999396 and (1.415)² = 2.002225. Therefore square root of 2 is

• exactly 1.414

• between 1.414 and 1.415

It can be proved that there is no terminating decimal that, when squared, equals exactly 2. So the decimal for square root of 2 in a square root table, when squared, equals

• exactly 2

• approximately 2

REMEMBER: Every rational number can be represented either by a terminating decimal or by a

• repeating decimal

• non-repeating decimal