Question

Can a radical with a negative radicand have a real square root? Why or why not?

A) Yes, because negative numbers have real square roots.
B) No, because the square root of a negative number is imaginary.
C) No, because the square root of a negative number is undefined in real numbers.
D) Yes, because all radicals have real square roots.

Answer 1

No, a radical with a negative radicand cannot have a real square root. The square root of a negative number is imaginary.

Step-by-step explanation:

No, a radical with a negative radicand cannot have a real square root. The square root of a negative number is imaginary. In real numbers, square root is only defined for non-negative numbers.

For example, let's consider the square root of -9. In real numbers, this does not have a real square root. However, we can express it as the imaginary number, √-9 = 3i, where i is the imaginary unit.

Therefore, the correct answer is B) No, because the square root of a negative number is imaginary.