Question

Can someone please show me step by step what to do? Please I'm really having a hard time understanding what it is I'm doing.
Simplify the radical expression. Assume that all variables represent positive real numbers.

Answer 1

\[2\sqrt{45z ^{2}a}+10z \sqrt{125a}\]

Answer 2

Hi, Scarlett,

What did you learn from the previous problem you posted here?
By now it should be clear that you need to examine the quantities under the radicals and determine the largest perfect square in each radicand. Have you done that yet?

Answer 3

factor 45 and 125 first so as to simplify the radicals
45 = 5 * 9
125 = 5 * 25

so sqrt125 = 5 sqrt5
and sqrt45 = 3 sqrt5

Answer 4

What is the largest perfect square factor of 45?
What is the same for z^2?
What is the same for 125?

Answer 5

Combine my questions with welshfella's demo and answers.

Answer 6

\[125=5\sqrt{5}\]
\[45=3\sqrt{5}\]

Answer 7

right - now what is the square root of z^2?

Answer 8

2?

Answer 9

???
does 2 * 2 = z^2

Answer 10

4z

Answer 11

still wrong
4z * 4z = 16z^2

Answer 12

square root of z^2 is simply z

Answer 13

because z * z = z^2 by definition

Answer 14

so can you simplify the first term

2sqrt ( 45z^2a)

Answer 15

\[2\sqrt{9\times5x ^{2}?}\]

Answer 16

its
2 * 3 * z * sqrt(5a)

Answer 17

do you follow that?

Answer 18

Okay back up really quick I'm lost

Answer 19

okay but wouldn't 3*2=6 and 5*5=25 sqrt z?

Answer 20

Oh whats wrong with me today - forget that 5!!!

2 *3 sqrt5 * z * sqrta

Answer 21

okay I'm starting to see it the problem

Answer 22

sqrt5 * sqrta = sqrt 5a

so we have

6 z sqrt (5a)

Answer 23

OK?

Answer 24

Yes

Answer 25

the second term is a little easier
can you figure it out?

Answer 26

Maybe

Answer 27

you already now that sqrt 125 = 5 sqrt5

Answer 28

right

Answer 29

Are we just trying to figure out what's in the square root first? Or do we add the 10 in the problem too?

Answer 30

10 z * 5 * sqrt 5 * sqrt a

Answer 31

- simplifying the square root bit first

Answer 32

check how we did the first term - this is very similar

Answer 33

okay the first one was 3*2 sqrt 5* z * sqrt a in this one the numbers are different it would be 5*2 sqrt 5 * 2 * sqrt a right?

Answer 34

No
not sure what you are thinking there we have

10 *z * 5 * sqrt5 * sqrta

first simplify the radical part then the other bits

Answer 35

so do don't simplify 10 when you find the radical (which I'm having a very help time doing)

Answer 36

sqrt5 * sqrt a = sqrt ?

Answer 37

its simply sqrt (5a)

Answer 38

and 10 *z * 5 = what?

Answer 39

50*5 maybe

Answer 40

No

why does the z disappear?

Answer 41

I meant 50*z sorry

Answer 42

right which is written as 50z

Answer 43

so we are lef twith

6 z sqrt5 + 50 z sqrt5


- 2 like terms so we just add them for the final answer

Answer 44

\[56\sqrt{5}\]

Answer 45

Why dont you like the z????

Answer 46

would the z go before 56 or after 5?

Answer 47

after the 56

Answer 48

ok so like \[56x \sqrt{5}\]

Answer 49

yea except it z not x

Answer 50

right sorry I'm use to x's not z's

Answer 51

gotta go
bye

Answer 52

Okay thanks for sticking with me I know I asked a lot of stupid questions

Answer 53

@Atrineas