Question

@mathmate

Answer 1

@mathmate

Answer 2

Chapter 9 ;-;

Answer 3

Chapter 9
======

Answer 4

Find x (hypotenuse) shown in the above drawing.

Answer 5

a^2 + b^2 = c^2?

Answer 6

Yep, now evaluate x numerically, please.

Answer 7

12^2+5^2=c^
144+25=169
13^2

Answer 8

So x=13 (is the final answer).

Answer 9

which two consecutive integers does sqrt(200) fall between?

Answer 10

idk this ;-;

Answer 11

10^2=100
11^2=121
12^2=144
13^2=169
14^2=196
15^2=225
16^2=256
...
which two consecutive integers does sqrt(200) fall between?

Answer 12

no .-.

Answer 13

*none

Answer 14

"between" is the keyword.
We know that 14^2=196, and 15^2=225
or sqrt(196)=14, sqrt(225)=15, so sqrt(200) falls between which integer numbers?

Answer 15

Decimals? .-.

Answer 16

wait no

Answer 17

no, we are looking for two integer numbers! lol

Answer 18

This si confusing T_T lets skip this

Answer 19

the answer is 14 and 15.
In fact sqrt(200)=14.1421356237309.... (never ends).
So we know that sqrt(200) falls between 14 and 15!
You were probably thinking that it's more complicated than this!

Answer 20

-_-

Answer 21

The hint is 14^2=196, so too small,
15^2=225, so too big.
Therefore sqrt(200) must fall between 14 and 15. Is that ok?

Answer 22

yes

Answer 23

Solve the equation 27-3y^2=0

Answer 24

Would you like the work or is it ok to put in the answer?

Answer 25

put in the work, but LaTeX is not required.

Answer 26

first find a GCF
27-3y^2=0
-3 is the gcf
then square root
answer: −3(y+3)(y−3)
set values to 0
y=3 or y=−3

Answer 27

/.\

Answer 28

Very good, shows that you're comfortable with factoring.
It will help in the later sections.

You can also solve by isolating y,
-3y^2=-27
y^2=9
y=\(\pm 3\)

Answer 29

Ready for the next one?

Answer 30

an engineering student is a contestant in an egg dropping contest. The goal is to create a container for an egg so it can be dropped from a height of 32 feet without breaking. The model for the egg's height, h (in feet), at time t seconds since release, is
h = -16t^2 + 32.

Calculate the time at whic the egg is at a height of 10 feet above ground. Give answer to 2 decimal places.

Answer 31

10=-16t^2+32
subtract 32 from both sides then divide by 16
1.375= t^2
idk where to go after this

Answer 32

Take out your ti-83 to finish!

Answer 33

"give answer to 2 decimal places" is a hint you might need your ti-83!

Answer 34

sqrt(1.375)=?

Answer 35

1.172604

Answer 36

exactly! (1.17 for 2 decimal places).

Answer 37

Any questions before we move to simplifying radicals?

Answer 38

no

Answer 39

Simplifying radicals basically is to pull things out of the square-root sign, whenever possible.
For example, sqrt(4)=2 is rather straight-forward.

Answer 40

But sqrt(18) is less obvious, since we write
sqrt(18)=sqrt(3^2 *2)=3sqrt(2)

Answer 41

So I'll let your try sqrt(48) while I take a meal break!

Answer 42

48
6 8
3 2 42
\[2\sqrt{12}\]

Answer 43

almost, just one step further
sqrt(48)=sqrt(4*12)=sqrt(16*3)=sqrt(4^2 * 3)=4sqrt(3)

Answer 44

Simplify
(1) sqrt(98) [98=2*7*7]

Answer 45

So every factor that appears twice inside the radical you take one outside.
So sqrt(98)=sqrt(2*7*7)=7sqrt(2)

Answer 46

Dance club.

Answer 47

Dance club is the method my teacher taught me because teens like to think like that

Answer 48

Oh! Can you show me that?

Answer 49

Ok its been a while but eh :P
56
8 7
4 2
2 2



2 and 2 are a couble so they leave the dance club
2 squrt 2
idk if its right

Answer 50

Yes, I get the part for the leaving dance club part (ingeneous!)
Then we have to keep 2*7 in the club, so we get
2sqrt(14)

Answer 51

lel :3

Answer 52

Are we done with this section ?

Answer 53

I usually like to see you do at least one perfect answer, like
(2) sqrt(60) [60=2*2 * 3 * 5]
then there is rationalize the denominator.

Answer 54

T_T

Answer 55

ok

Answer 56

(2) sqrt(60) [60=2*2 * 3 * 5]

Answer 57

im confused whats the question? .-.

Answer 58

simplify sqrt(60)

Answer 59

60
10 6
5 2 3 2
2 sqrt 15

Answer 60

T_T say im right!

Answer 61

Princess demands it!

Answer 62

Yes, you're right, I don't think you have problem with that.

Answer 63

Now we move onto rationalizing the denominator.

Answer 64

Mathematicians traditionally do not like to see square roots in the denominator, because that would make the common denominator very messy.

Answer 65

Just multiply by the root

Answer 66

*in the denominator

Answer 67

Do you want me to explain, or jump to pretest?

Answer 68

Pretest

Answer 69

Rationalize 9sqrt(1/3)

Answer 70

9 squrt 3

Answer 71

^LOL

Answer 72

Sure?

Answer 73

The question was \(9\sqrt{\frac{1}{3}}\)

Answer 74

:/

Answer 75

this is diffrent .-.

Answer 76

Example:
\(sqrt(\frac{2}{5}) = \frac{\sqrt2}{\sqrt5}=\frac{\sqrt2\times \sqrt5}{\sqrt5^2}=\frac{\sqrt{10}}{5}\)

Answer 77

just a recap,
we were working on simplify 9sqrt(1/3).
I sent this previous example to help.

Answer 78

sqrt 3/ 3

Answer 79

9 sqrt(1/3) = 9(sqrt(1)/sqrt(3)) = 9(sqrt(1)*sqrt(3)/(sqrt(3)^2)=9sqrt(3)/3=3sqrt(3)

Answer 80

or
\(9\sqrt{1/3}=3\frac{\sqrt3 \times \sqrt3}{\sqrt3}=3\sqrt3\)

Answer 81

IM IRGHT??

Answer 82

*RIGHT?

Answer 83

no, you had the 3 as denominator, and not multiplied.

Answer 84

>:(

Answer 85

9

Answer 86

.-.

Answer 87

not 9, it's \(3\sqrt3\) :)

Answer 88

>:(

Answer 89

ok, try this one:

Simplify \(\Large \sqrt{\frac{25}{3}}\)

Answer 90

\[\huge~\frac{ 5\sqrt{3} }{ 3 }\]

Answer 91

Am i right?