Question

How do I factor 5 sq root 24 times 3 sq root 10

Answer 1

\[5\sqrt{24} \times 3\sqrt{10}\]

Answer 2

If you are looking for the answer to (5sqrt24) x (3sqrt10) the answer is 54,000

Answer 3

How did you get that?

Answer 4

i got this by multiplying

Answer 5

It might help to simplify first before you multiply. So let's simplify \(\large \sqrt{24}\) first.

\[\large \sqrt{24} = \sqrt{4*6}\]

\[\large \sqrt{24} = \sqrt{4}*\sqrt{6}\]

\[\large \sqrt{24} = 2\sqrt{6}\]

Notice how I factored 24 into 4*6 and 4 is a perfect square.

Answer 6

Since 10 doesn't have any factors which are perfect squares (other than 1), this means that \(\large \sqrt{10}\) cannot be simplified

Answer 7

So that means we'll have this


\[\large 5\sqrt{24} \times 3\sqrt{10}\]


\[\large 5*2\sqrt{6} \times 3\sqrt{10}\]


\[\large 10\sqrt{6} \times 3\sqrt{10}\]


\[\large (10*3)*(\sqrt{6}*\sqrt{10})\]


\[\large 30\sqrt{6*10}\]


I'll let you finish up.

Answer 8

Now if I have \[2\sqrt{6}\]
can i multiply it with \[3\sqrt{10}\]?

Answer 9

yes you can

Answer 10

you do so by multiplying the outer coefficients together

Answer 11

then combining the roots using the idea that \(\large \sqrt{x}*\sqrt{y} = \sqrt{x*y}\)

Answer 12

\[6\sqrt{60}\]

Answer 13

Don't forget about the 5 as well

Answer 14

60= 2,30= 2,15 = 3,5
2 \[\sqrt{60}=2\sqrt{15}\]

Answer 15

what five?

Answer 16

wait so the answer is 12 sq root 15?

Answer 17

up at the top you have "5 sq root 24 times 3 sq root 10"

so the first number in the expression

Answer 18

oh yeah

Answer 19

so it's 30 sq root 60?

Answer 20

now simplify \(\large \sqrt{60}\)

Answer 21

\[30\sqrt{60}=30(2\sqrt{15})=60\sqrt{15}\]

Answer 22

you are correct, the final answer is \(\large 60\sqrt{15}\)

Answer 23

could you help me with one more similar problem really quick?

Answer 24

sure

Answer 25

go for it

Answer 26

\[\sqrt{3}\times \sqrt{27}\]

Answer 27

I would simplify \(\large \sqrt{27}\) first

Answer 28

or I guess you could just combine the roots and multiply

Answer 29

either way works

Answer 30

so i would just make it
\[\sqrt{3}\times3\sqrt{3}\]

Answer 31

then you combine the roots and multiply

Answer 32

which is just 3 * 3 =9

Answer 33

then take the square root of that to get 3

Answer 34

oh snap I forgot about that okay that makes sense

Answer 35

that's ok, i have brain farts all the time too

Answer 36

could you help me with one last question? i swear thats it after this

Answer 37

sure I'd love to

Answer 38

\[\frac{ 3 + \sqrt {7}}{ 2 - \sqrt 10 }\]

Answer 39

i know i have to multiply the top and bottom by 2 + sqrt 10

Answer 40

good start, what does that give you once you do?

Answer 41

\[\frac{ 6+ 3\sqrt10 +2\sqrt7+\sqrt70 }{ 4 - \sqrt10 + \sqrt10 - \sqrt100}\]

Answer 42

And then i'd combine all the like terms

Answer 43

so far, so good

Answer 44

keep going

Answer 45

to get
\[\frac{ 6 + 3\sqrt7+2\sqrt7+\sqrt70 }{ -6 }\]

Answer 46

and that's where I'm stuck

Answer 47

what are the like terms in this case?

Answer 48

6?

Answer 49

what else

Answer 50

sqrt 7?

Answer 51

correct, if you replace \(\large \sqrt{7}\) with z (or any other variable really), you go from

\[\large 3\sqrt7+2\sqrt7\]

to

\[\large 3z + 2z\]

and that looks much clearer in terms of spotting the like terms (and combining them)

Answer 52

so would i multiply those two and get (3 * 2) (sqrt7 * sqrt7) = 6*7=42?

Answer 53

nope, look at my last message

Answer 54

wait no i wrote that wrong it's supposed to be
\[\frac{ 6+3\sqrt10+2\sqrt7+\sqrt70 }{ -6 }\]

Answer 55

oh right, not sure where the root 10 went...

Answer 56

at this point, there's not much you can do

Answer 57

I just wrote it down wrong. This is where I have trouble simplyfing it.

Answer 58

because there are no like terms in the numerator

Answer 59

what bout the 6 and -6?

Answer 60

*about

Answer 61

I guess you could go from

\[\frac{ 6+3\sqrt{10}+2\sqrt{7}+\sqrt{70} }{ -6 }\]

to

\[\frac{ -6-3\sqrt{10}-2\sqrt{7}-\sqrt{70} }{ 6 }\]

Answer 62

but that's about all you can do really

Answer 63

i thought you could get rid of the 6 and 6

Answer 64

if you do that, you would have to break up the fraction

Answer 65

oh whoops

Answer 66

okay that's it haha thank you so much for all the help I really appreciate it

Answer 67

You're welcome, I'm glad I could be of help.

Answer 68

Have a nice night or day wherever you are

Answer 69

thanks, you too