does the square root of 15/25 have an infinite or finite decimal expansion

3 answers

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.