9514 1404 393
Answer:
D. √2
Step-by-step explanation:
Any finite-length decimal number, positive or negative, is rational. The square root of a perfect square, such as √4 = √(2²) = 2, is also a rational number.
The number 2 is not a perfect square, so its square root is irrational.
The only irrational number on the list is √2, choice D.
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<em>Additional comment</em>
Your calculator can help you identify square roots (and other roots) that are irrational. If the square root has more digits in its decimal fraction than the original number does, then it is irrational.
<u>Examples</u>:
√6.25 = 2.5 . . . . root has 1 decimal digit, original number has 2. This number is rational.
√6.24 ≈ 2.49799919936 . . . . root has an infinite number of decimal digits. The number shown is limited by the available calculator display. It is more digits than the original number has. This number is irrational.
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If a number with a decimal fraction is a perfect square, the number of fractional digits in its square root will be half as many as in the original number. Above, 6.25 has 2 fractional digits; its root 2.5 has 1 fractional digit--half as many. (A rational cube root will have 1/3 as many fractional digits.)
