A few more questions
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
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.
-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
then (3/2)2*e-6f-2g-6
of course, you could move the negative exponents to the denominator.
1. To describe the negative square root of 47, we need to determine its classification among the given options: Natural, Whole, Integer, Rational, Irrational, and Real.
The negative square root of a non-perfect square like 47 is an example of an irrational number. Irrational numbers are numbers that cannot be expressed as a fraction, and they have non-terminating and non-repeating decimal expansions.
To confirm this classification, you can use the fact that the square root of 47 is irrational. Since multiplying by -1 doesn't change the classification, the negative square root of 47 remains irrational. Therefore, the correct classification for the negative square root of 47 is irrational.
2. To simplify the expression (2ef^-3 * g^(2/3)e^-2 * f^4 * g)^-2, we can follow the order of operations (PEMDAS/BODMAS):
- Simplify within parentheses (if any).
- Evaluate exponents.
- Perform multiplication and division from left to right.
- Perform addition and subtraction from left to right.
Let's break down the process step by step:
Step 1:
In the expression (2ef^-3 * g^(2/3)e^-2 * f^4 * g)^-2, we have an exponent of -2 outside the parentheses. This means we need to apply the exponent to everything inside the parentheses.
Step 2:
Within the parentheses, we can simplify each term separately:
- (2ef^-3) remains as it is.
- g^(2/3)e^-2 can be rewritten as (g^(2/3) * e^-2).
Step 3:
Now, we can simplify further:
- (g^(2/3) * e^-2) can be written as (g^(2/3) / e^2) since the negative exponent flips the fraction.
Step 4:
With these simplified terms, we can rewrite the expression as follows:
(2ef^-3 * g^(2/3) / e^2 * f^4 * g)^-2.
Step 5:
Now, we can apply the exponent of -2 to everything within the parentheses:
1 / (2ef^-3 * g^(2/3) / e^2 * f^4 * g)^2.
Step 6:
To simplify further, we can square each term within the parentheses:
1 / (4e^2f^-6 * g^(4/3) / e^4 * f^8 * g^2).
Step 7:
Finally, we can bring everything together by multiplying and dividing as needed:
1 / (4e^2e^4f^-6f^8g^(4/3)g^2).
Step 8:
To simplify, we can combine the exponent terms and cancel out any like terms in the numerator and denominator:
1 / (4e^6f^2g^(4/3)g^2).
The resulting expression after simplification is 1 / (4e^6f^2g^(4/3)g^2).