Question

Write a radical expression without a coefficient other than 1 that, when simplified, the answer is 15i.

Option 1: √15i
Option 2: √5i
Option 3: 15√i
Option 4: 5√3i

Answer 1

No given option simplifies directly to 15i. A correct expression, not listed in the options, would be √225i, which simplifies to 15i.

Step-by-step explanation:

The question asks to choose a radical expression without a coefficient other than 1 that simplifies to 15i. To solve this question, we recall that multiplying square roots with the same base can be done by adding their exponents. For example, 5¹ × 5¹ simplifies to 5 since the exponents add up to 1. Similarly, if we need to simplify a square root expression with a complex number, we look for a radical that when multiplied by itself will give us the desired result. Let's break down the fourth option 5√3i to test if it works:

1. Multiply 5 by itself to get 25.
2. √3i × √3i simplifies to 3i since we have (i¹ × i¹ = i).
3. Thus, 25 × 3i simplifies to 75i.
4. However, to get 15i, we need a factor of 1 instead of 5, so the correct option is actually √225i, which is equivalent to √(15²) × √i. This simplifies to 15i since (√15² = 15) and (√i = i).

None of the given options correctly simplifies to 15i. A correct expression, not provided in the options, would be √225i, which would simplify to 15i.