Answer:
A) yes. √2.89 = 1.7
B) no. √0.004 = (√10)/50, an irrational number
Step-by-step explanation:
You want to know if 2.89 and 0.004 are perfect squares, and why or why not.
Perfect square
A number is considered to be a perfect square if it has a rational square root. Usually, we use the term perfect square to refer to the squares of integers. However, the square of any rational number can be considered to be a perfect square.
A number is not a perfect square if its root is irrational.
A) 2.89
The root of 2.89 is 1.7. 2.89 has a rational square root, so can be considered to be a perfect square.
B) 0.004
The root of 0.004 is (√10)/50. The square root of 10 is irrational, so 0.004 is not considered to be a perfect square.
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Additional comment
The number of decimal digits in the fractional portion of the square root of a decimal will be half the number of the digits in its decimal portion. That is, the number 0.0040 will have 2 decimal digits in its root if it is a perfect square. For example, √0.0036 = 0.06. If your calculator tells you the root has more digits than this, the number is not a perfect square.
You will notice 2.89 has 2/2 = 1 decimal digit in its root, 1.7.
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