College

Which choice is equivalent to the expression below?

\(\sqrt{-18}\)

A. \(18i\)
B. \(-3\sqrt{2}\)
C. \(-18i\)
D. \(3\sqrt{2}i\)

Answer :

Final answer:

The expression √-18 is equivalent to 3i√2.


Explanation:

The square root of a negative number is not a real number, but it can be represented using the imaginary unit 'i'. The expression √-18 can be written as 3i√2, which is equivalent to choice OE.


Learn more about Square roots of negative numbers

Final answer:

The equivalent expression for √-18 is 3√2i, as √-18 can be simplified to 3√2 * i, which corresponds to choice OE in complex numbers.

Explanation:

The expression √-18 involves the square root of a negative number, which is not possible in the set of real numbers. However, by using complex numbers, where i is defined as the square root of -1, such an expression can be evaluated.

First, we can simplify √-18 by separating it into two parts: the square root of -1, which is i, and the square root of 18. The number 18 can be factored into 9 * 2, which allows further simplification because 9 is a perfect square.

√-18 = √(9 * 2 * -1) = √9 * √2 * √-1 = 3√2 * i

Therefore, the equivalent expression for √-18 in terms of complex numbers is 3√2i, which corresponds to choice OE.