Question

i give medals and fans to people who help me
please
question 1
Part 1: Explain, in complete sentences, how you might show that radicals should be simplified before being added or subtracted to another radical. (2 points)

Part 2: Give an example of an addition or subtraction problem of radicals where this would apply. (2 points)

question 2
Part 1: Explain, in complete sentences, the purpose of converting a radical expression into a rational exponent. (2 points)
Part 2: Give an example. (2 points)

Answer 1

@John_ES can you help me

Answer 2

Question 1:
Part 1
Radicals can be simplified, dividing the numerator and denominator by their maximum common divisor.

Part 2
A pastel is divided into six parts. Mary takes 2 parts of the cake and then the third part of the rest of the cake. Writes the fraction that represent the total quantity consumed
Solution:
First: 2/6
Second:\[\frac{1}{3}(1-\frac{2}{6})=\frac{4}{18}\]
Total consumed \[\frac{1}{6}+\frac{4}{18}=\frac{1}{6}+\frac{2}{9}=\frac{7}{18}\]

Where we have simplified 4/18, using the MCD(4,18)=2.

Question 2
Part 1
A radical expression should be converted into a rational exponent in order to apply the properties of the laws of exponentiation. For example, the product of two radicals with the same basis is a radical with the same base and a exponent that is the result of the sum of the exponents.

Part 2
\[\sqrt[3]2\cdot\sqrt[5]{2}=2^{1/3}\cdot2^{1/5}=2^{7/10}=\sqrt[10]{2^7}\]

(Hope it helps ;))

Answer 3

In the part 2, it should be,
\[\sqrt[3]{2}\cdot\sqrt[5]{2}=2^{1/3}\cdot 2^{1/5}=2^{8/15}=\sqrt[15]{2^8}\]