Which of the following is an irrational number?
a. negative square root of 5
B. 1/8
c. 0.3858585...
d. negative square root of 64
An irrational number is a number that cannot be expressed as a fraction or a decimal with a finite number of digits after the decimal point, and it does not repeat periodically.
In the given options, the negative square root of 5 would be an irrational number because √5 is irrational and taking the negative of it would still result in an irrational number.
Therefore, the answer is option a. negative square root of 5.
To determine which of the given options is an irrational number, we need to understand what an irrational number is. An irrational number is a number that cannot be expressed as a fraction (ratio) of two integers and has an infinite non-repeating decimal representation.
Now let's analyze each option:
a. The negative square root of 5: This option represents the square root of 5, which is approximately 2.23606. Since the square root of 5 cannot be expressed as a fraction and has a non-repeating decimal representation, it is an irrational number.
b. 1/8: This option is a fraction representing the division of 1 by 8. Fractions are rational numbers by definition, not irrational numbers. Therefore, this option is not an irrational number.
c. 0.3858585...: This option is a decimal representation with a repeating pattern. Even though it is an infinite decimal, it has a repeating pattern, making it a rational number rather than an irrational number.
d. The negative square root of 64: This option represents the square root of 64, which is 8. Since 8 can be expressed as the fraction 8/1, it is a rational number, not an irrational number.
Therefore, the correct answer is option a. The negative square root of 5 is an irrational number.