does the square root of 15/25 have an infinite or finite decimal expansion
The square root of 15/25 does not have an infinite decimal expansion.
To find the square root of 15/25, we simplify the fraction first:
√(15/25) = √(3/5)
Since the square root of 3/5 is an irrational number, the decimal expansion will continue indefinitely without repeating. Thus, the square root of 15/25 has an infinite decimal expansion.
Dos the square root pf 5/16 have an infinite or finite decimal expansion
The square root of 5/16 has an infinite decimal expansion.
To find the square root of 5/16, we simplify the fraction first:
√(5/16)
Taking the square root of 5 and 16 individually, we get:
√5 / √16
√5 is an irrational number, so its decimal expansion is infinite.
The square root of 16 is 4, which has a finite decimal expansion.
Therefore, the square root of 5/16 is the irrational number (√5)/4, which has an infinite decimal expansion.
To determine if the square root of 15/25 has an infinite or finite decimal expansion, let's calculate the square root.
First, simplify the fraction 15/25 by dividing both the numerator and denominator by 5. This gives us 3/5.
Now, let's calculate the square root of 3/5. Taking the square root of a fraction means taking the square root of the numerator and the square root of the denominator separately.
The square root of 3 is an irrational number and cannot be expressed as a finite decimal. Therefore, when we calculate the square root of 3/5, the decimal expansion will be infinite rather than finite.