Answer :

The equivalent expression for "[tex]$$\sqrt{-9g}$$[/tex]" is 3i√g. This represents a complex number with a real part of 0 and an imaginary part of 3√g, demonstrating that the square root of a negative number can be expressed using imaginary numbers. Here option B is correct.

The expression [tex]$$\sqrt{-9g}$$[/tex] involves the square root of a negative number, which is not defined in the real number system. However, in the realm of complex numbers, we can use the imaginary unit i, where i^2 = -1.

First, we can rewrite [tex]$$\sqrt{-9g}$$[/tex] as [tex]$$\sqrt{-1} \sqrt{9} \sqrt{g}$$[/tex], utilizing the property that [tex]$$\sqrt{ab} = \sqrt{a} \sqrt{b}$$[/tex]. This gives us [tex]$$i \cdot 3 \cdot \sqrt{g}$$[/tex], since [tex]$$\sqrt{-1} = i$$[/tex] and [tex]$$\sqrt{9} = 3$$[/tex]. Simplifying further, we get [tex]$$3i \sqrt{g}$$[/tex].

So, the equivalent choice is B. i√g. This represents a complex number with a real part of 0 and an imaginary part of [tex]$$3\sqrt{g}$$[/tex], showing that the square root of a negative number can indeed be expressed using imaginary numbers. Here option B is correct.

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Hey there!!

Remember - i = √-1

√-81 can be written as

√-1 × √81

√81 = 9

and √-1 = i

Final answer - 9i

Option c

Hope it helps!