Question

precalculus help! i'm having some trouble with my summer assignment. help would be very appreciated :)))

Answer 1

Problem 3:

We are given the following complex number and I'm assuming we want to simplify it:

$\dfrac{5+i}{6+i}$

Using the complex arithmetic rule (research about this if you're not familiar with it, it's very helpful):

$=\dfrac{(5\times6+1)+(6-5)i}{6^2+1^2}$

$=\dfrac{31+i}{37}$

Simplifying gives us:

$=\dfrac{31}{37}+\dfrac{1}{37}i$

Problem 6:

You seem to have done this problem correctly

$\sqrt[8]{8y^{16}}$

Expanding gives us:

$=\sqrt[8]{y^{16}}\times\sqrt[8]{8}$

$=y^2\sqrt[8]{8}$

This can't be simplified further as the 8th root of 8 gives us an irrational number

Let me know if you need any clarifications or extra help, thanks!

Answer 2

6.

$y^2\sqrt[8]{8}$

Step-by-step explanation:

$\sqrt[8]{8*y*y*y*y*y*y*y*y*y*y*y*y*y*y*y*y}$

Since there are eight y's in two groups we can take them out which turns into

$y^2\sqrt[8]{8}$

:)

3.