Part A - The sum of 2√5 and 3√16 in its simplest form is 2(√5 + 6).
The given numbers are surds.
To find the sum of 2√5 and 3√16, we perform the arithmetic operation of addition on the surds.
So, 2√5 + 3√16 = 2√5 + 3 × 4 (√16 = 4)
2√5 + 3√16 = 2√5 + 12
Factorizing out the factor 2 from both expressions, we have
2√5 + 3√16 = 2√5 + 6 × 2
2√5 + 3√16 = 2(√5 + 6)
So, the sum of 2√5 and 3√16 in its simplest form is 2(√5 + 6).
Part B - The result is irrational.
The result is irrational because 2(√5 + 6) cannot be expressed as a ratio of two integers since √5 is irrational and √5 + 6 is irrational and thus 2(√5 + 6) is also irrational since it cannot be expressed as a ratio of two integers. Also, its decimal representation is non-terminating or repeating.
Thus, the result is irrational.
Learn more about surds here:
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