Question

current objective
simplify numerical expressions with higher roots

question
simplify: \\(\sqrt4{-1296}\\).

select the correct answer below:
6
36
-6
-216
not a real number

Explanation:

Identify the index and the radicand

$$ \sqrt[4]{-1296} $$

Index: \(n = 4\) (even)
Radicand: \(x = -1296\) (negative)

Apply the rule for even roots of negative numbers

An even root of a negative real number is not a real number.

$$ \sqrt[2k]{-a} otin \mathbb{R} \quad \text{for } a > 0, k \in \mathbb{Z}^+ $$

Answer:

• (A) 6
• (B) 36
• (C) \(-6\)
• (D) \(-216\)
• (E) not a real number (Correct answer)