Question

Alg 1 Honors Help Please

What is the exact value of the expression the square root 72. − the square root of 8. + the square root of 128.? Simplify if possible.

8the square root of 2.

12the square root of 2.

8the square root of 3.

12the square root of 3.


What is the exact value of the expression the square root of 9 times y to the fourth power. + 12the square root of y to the sixth power. − 3the square root of y to the sixth power. − the square root of y to the fourth power.? Simplify if possible.

8y2 + 9y3

11y2

11y5

2y2 + 9y3

Answer 1

@Hero @radar @jim_thompson5910 Can you guys help me please?

Answer 2

what do you get when you simplify \[\large \sqrt{72}\]

Answer 3

√9*8

Answer 4

keep going

Answer 5

all the possible ones for 72? or do you mean keep going with 8

Answer 6

actually it would be better to write 72 as 36*2

Answer 7

like this

\[\large \sqrt{72} = \sqrt{36*2}\]

\[\large \sqrt{72} = \sqrt{36}*\sqrt{2}\]

\[\large \sqrt{72} = 6\sqrt{2}\]

Answer 8

ohh! and for 8, \[2\sqrt{2}\]

Answer 9

good, you're getting the hang of this

Answer 10

how about sqrt(128)

Answer 11

For 128, \[2\sqrt{32}\]

Answer 12

you can keep going

Answer 13

\[1\sqrt{16}\]

Answer 14

hmm not sure how you're getting that

Answer 15

hint: 128 = 64*2

Answer 16

the idea is to factor the number into 2 numbers where one of the numbers is the largest possible perfect square possible

Answer 17

ohh! \[8\sqrt{2}\]

Answer 18

good

Answer 19

\[12\sqrt{2}\]

Answer 20

is the final answer?

Answer 21

so

\[\large \sqrt{72} - \sqrt{8} + \sqrt{128}\]

turns into

\[\large 6\sqrt{2} - 2\sqrt{2} + 8\sqrt{2}\]

Answer 22

yep, then you combine like terms to get

\[\large 6\sqrt{2} - 2\sqrt{2} + 8\sqrt{2} = 12\sqrt{2}\]

Answer 23

Thank you so much! Can you help me with a few more problems please?

Answer 24

sure, but just a few though

Answer 25

what else do you need help with

Answer 26

Brian is creating a collage on a piece of cardboard that has an area of 150r2 square centimeters. The collage is covered entirely by pieces of paper that do not overlap. Each piece has an area of the square root of r cubed square centimeters. Use the given information to determine an expression for the total number of pieces of paper used.

Answer 27

here's a similar example

Answer 28

let's say that each piece of paper covers an area of 10 square cm

if the papers don't overlap and they cover the entire board that's 270 square cm

then this means that you would need 270/10 = 27 sheets of paper

Answer 29

put another way

(Total Area of Board) = (# of sheets of paper)*(area of one sheet of paper)

and you can solve/rearrange things to get

(# of sheets of paper) = (Total Area of Board)/(area of one sheet of paper)

Answer 30

make sense?

Answer 31

Kind of

Answer 32

what's not making sense

Answer 33

yup i get it

Answer 34

you sure?

Answer 35

Yupp.

Answer 36

ok so in our case, the total area is 150r^2

the area of each piece is sqrt( r^3 )

Answer 37

if x = # of sheets of paper, then,

(Total Area of Board) = (# of sheets of paper)*(area of one sheet of paper)

( 150r^2 ) = ( x )*( sqrt( r^3 ) )

150r^2 = x *sqrt( r^3 )

now solve for x

Answer 38

First, isolate the x. That makes the equation x=√(r^3) - 150 r^2

Answer 39

no, but that's a good try

Answer 40

the symbol * means "times"

Answer 41

ex: 2 * 3 = 2 times 3 = 6

Answer 42

so if you have something like

10 = x*2

then how do you isolate x?

Answer 43

x=10/2

Answer 44

good, you divide to undo multiplication

Answer 45

so how can you apply that idea to 150r^2 = x *sqrt( r^3 ) so you can solve for x

Answer 46

x=\[\frac{ 150r^2 }{ \sqrt{r^3} }\]

Answer 47

very good, now rationalize the denominator

Answer 48

and simplify

Answer 49

r*r*r

Answer 50

it might help to simplify sqrt(r^3) first

Answer 51

doing so will give you

\[\large \sqrt{r^3} = \sqrt{r^2*r}\]

\[\large \sqrt{r^3} = \sqrt{r^2}*\sqrt{r}\]

\[\large \sqrt{r^3} = r\sqrt{r}\]

Answer 52

so

\[\large x = \frac{150r^2}{ \sqrt{r^3} }\]

becomes

\[\large x = \frac{150r^2}{ r\sqrt{r} }\]

Answer 53

yuppp

Answer 54

then that turns into

\[\large x = \frac{150r}{\sqrt{r} }\]

I'll leave the last part to you

Answer 55

x=150?

Answer 56

I dont know how to divide with roots. :/

Answer 57

how would you rationalize the denominator

Answer 58

\[\frac{ \sqrt{r} }{ 150r}\]

Answer 59

no

Answer 60

you need to multiply top and bottom by sqrt(r)

Answer 61

then simplify

Answer 62

\[\frac{ 150r }{ r }\times \frac{ \sqrt{r} }{ \sqrt{r}} \]

Answer 63

oops forgot the √ for the bottom one

Answer 64

that's ok, i know what you meant

Answer 65

keep going

Answer 66

I dont know how to multiply √r.

Answer 67

what is √r times √r.

Answer 68

√r^2

Answer 69

which simplifies to what

Answer 70

assume r > 0

Answer 71

1√r?

Answer 72

square roots undo squaring

Answer 73

√r/1

Answer 74

ex:

5 squared = 5^2 = 5*5 = 25

the square root of 25 = sqrt(25) = 5

Answer 75

√r * √r

Answer 76

so

sqrt( x^2 ) = x

assuming x > 0

Answer 77

which means

sqrt( r^2 ) = r

where r > 0

Answer 78

so we've gone from

\[\large x = \frac{150r}{\sqrt{r} }\]

to

\[\large x = \frac{150r\sqrt{r}}{r }\]

after multiplying top and bottom by sqrt(r)

Answer 79

what's the last step

Answer 80

x=150√r

Answer 81

very good

Answer 82

so you need \(\large 150\sqrt{r}\) sheets of paper

Answer 83

YASYDYAYAYASYYy THANK YOU!!!:)

Answer 84

lol glad I could be of help

Answer 85

Aww Thank you so much for saving me.

Answer 86

didn't do much really, but you're very welcome