A few more questions

Question

1. How do you describe the negative square root of 47? I said that it was imaginary, but I got one point marked off for my answer. The descriptions we could choose were Natural, Whole, Integer, Rational, Irrational, and Real. What is the correct classification?

2. I am supposed to simplify 2ef^-3 times g^2/3e^-2 times f^4times g, the whole expression to the negative second power. What would be the correct answer? How is it obtained?

Thanks

Answer 1

don't confuse "the negative square root of 47", which is -√47 or -6.85565..
with "the square root of -47" or √-47, which is imaginary.

Answer 2

-sqrt47 is not imaginary. It is real, and irrational.
sqrt(-47) is imaginary.

(2ef^-3*g²/3e^-2 * f⁴ * g)^-2

first do the inner..
(2/3 * e¹⁺²f^-3+4g²⁺¹)^-2

Answer 3

then (3/2)²*e^-6f^-2g^-6

of course, you could move the negative exponents to the denominator.