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Which of the following is a radical equation?

Ask by Carrillo Little. in the United States

Jan 21,2025

Question

11 12 13 14 15 16 17 18 19 Which of the following is a radical equation? $$ x+\sqrt{5}=12 $$ $$ x^{2}=16 $$ $$ 3+x \sqrt{7}=13 $$

UpStudy AI · Accepted Answer

A **radical equation** is one in which the variable appears inside a radical (such as a square root, cube root, etc.). Let's examine each of the provided equations:

1. **$$ x + \sqrt{5} = 12 $$**
   - Here, $$ x $$ is **not** inside a radical. The equation involves adding a constant radical ($$ \sqrt{5} $$) to the variable $$ x $$, but the variable itself is not under the radical sign.

2. **$$ x^{2} = 16 $$**
   - This is a **quadratic equation**, not a radical equation. The variable $$ x $$ is raised to a power, but it is not inside a radical.

3. **$$ 3 + x \sqrt{7} = 13 $$**
   - In this equation, $$ x $$ is multiplied by $$ \sqrt{7} $$, but again, $$ x $$ is **not** inside the radical. The radical is applied only to the constant $$ 7 $$, not to the variable $$ x $$.

**Conclusion:**
None of the provided equations are radical equations because the variable does not appear inside a radical. A classic example of a radical equation would be something like $$ \sqrt{x} + 2 = 5 $$, where $$ x $$ is directly under the square root.

**Answer:**  
None of the given equations qualify as a radical equation because the variable does not appear inside a radical.
None of the equations are radical equations because the variable does not appear inside a radical.

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Which of the following is a radical equation?

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