Which expression results in a rational number?
1 answer:
Answer:
option D is rational
Step-by-step explanation:
A rational number is a number that can be written in the form of fraction or integer
here in the given question
A) 1.5 + √1.5
now,
√1.5 is not rational as √1.5 = 1.2247448713915890490986420373529
hence A is not rational
b) 12 - √12
√12 is not rational as √12 = 3.4641016151377545870548926830117
hence B is not rational
c)
here,
is not rational
D)
now,
√25 = 5
hence,
=
= 5
therefore,
option D is rational
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LCM stands for least common multiple, and so the LCM of two number is the smallest possible common multiple of the two numbers.
Since 16 is already a multiple of 8 (and since every number is a multiple of itself), the LCM between 8 and 16 is sixteen itself: it is a multiple of 8, it is a multiple of 16, and there couldn't be a smaller one.
Even though this case was trivial, let's do the computation to learn how to do this in general: first of all, you need the prime factorizations of the two numbers:
The LCM of the two numbers is composed by all the primes appearing in any of the two factorizations. In case a prime appears in both factorizations, we choose the one with higher exponents.
In this case, 2 is the only prime to appear in both factorizations. So, we choose the one with higher exponent, which is 4, and the answer is , as we already observed.