Question

test information
description
instructions
timed test this test has a time limit of 1 hour and 40 minutes. the test will save and submit automatically when the time expires. warnings appear when half the time, 5 minutes, 1 minute, and 30 seconds remain.
multiple attempts this test allows multiple attempts.
force completion this test can be saved and resumed at any point until time has expired.
your answers are saved automatically.
remaining time: 1 hour, 26 minutes, 49 seconds.
question completion status:
moving to another question will save this response.
question 9
let x and y be real numbers. then it is true that $sqrt3{x + y}=sqrt3{x}+sqrt3{y}$.
true
false
moving to another question will save this response.

Explanation:

Step1: Test with counter - example

Let \(x = 1\) and \(y = 8\).
Then \(\sqrt[3]{x + y}=\sqrt[3]{1 + 8}=\sqrt[3]{9}\approx2.08\).
And \(\sqrt[3]{x}+\sqrt[3]{y}=\sqrt[3]{1}+\sqrt[3]{8}=1 + 2=3\).
Since \(\sqrt[3]{9}
eq3\), the equation \(\sqrt[3]{x + y}=\sqrt[3]{x}+\sqrt[3]{y}\) is not true for all real numbers \(x\) and \(y\).

Answer:

False