Question

could someone help me with simplifying radicals

Answer 1

& multiplying radicals?

Answer 2

I can do my best. Lets see what you need help with.

Answer 3

the equation is: multiply \[5\sqrt{8} * 4\sqrt{7}\]

Answer 4

It's 40sqrt14

Answer 5

could you explain how you did it?

Answer 6

We try and guide to answers here, not just give them.
You multiply the values out of the square root.
5*4=20
And inside,
7*8=56
\[20\sqrt{56}\]
\[20\sqrt{4\times 14}\]

Answer 7

\[40\sqrt{14}\]

Answer 8

I used a scientific calculator lol

Answer 9

sure.
first, you multiply the similar elements. so:
5 x 4 x sqrt(8x7)
That becomes 20 sqrt56

and then you simplify and get 40sqrt14

Answer 10

@xochital if the roots are the same, that is square or cube or else
then you multiply the OUTSIDE by the OUTSIDES and the INSIDE by the others INSIDES

Answer 11

\[\sqrt{4} = 2\] and you move that outside the square root.
\[20\times 2\sqrt{14} = 40\sqrt{14}\]

Answer 12

yeah, true @austinL. It's just preference that I give the answer first.

Answer 13

thank you all so much :)

Answer 14

No problemo!

Answer 15

so would \[\sqrt{3} * \sqrt{5}\] ?

Answer 16

that would equal \[\sqrt{15}\]
or something else ?

Answer 17

\[\sqrt{3}\times \sqrt{5}=\sqrt{3\times 5}=\sqrt{15}\]
Correct.

Answer 18

okay, do you mind helping me with a few more?

Answer 19

Sure, I don't mind at all.

Answer 20

okay thank you so much. for \[5\sqrt{3}(2\sqrt{3}+6\sqrt{19})\] would i have to distribute the \[5\sqrt{3}\]

Answer 21

Yes you would.
a(b+c) = ab + ac

Answer 22

then it would be ... \[10\sqrt{9}*30\sqrt{57}\].... how would i simplify that?

Answer 23

First, sqrt(9) = ?

Answer 24

3

Answer 25

Correct.10*3=30

Answer 26

\[30 + 30\sqrt{57}\] The second half cannot be simplified.

Answer 27

oh okay... how would i solve \[3x \sqrt{2}*\sqrt{14x}\]

Answer 28

\[3x\sqrt{2\times 14x} = 3x\sqrt{28x}\]
\[\sqrt{28} = 2\sqrt{7}\rightarrow3x\times2\sqrt{7} = 6x\sqrt{7x} = 6x\sqrt{7} \times x^{\frac{1}{2}} = 6\sqrt{7}\times x^{\frac{3}{2}}\]

Answer 29

one of the choices is \[6x \sqrt{7x}\] that's the correct answer then, right?

Answer 30

Well, then that is it. I went further than your question required I guess :P

Answer 31

hahha yes i guess you did :) one last question... \[\sqrt{2}(x-\sqrt{5})\]

Answer 32

would it be \[\sqrt{2x} - \sqrt{10}\]?

Answer 33

and then if i simplified that further it would come to \[\sqrt{2x} - \sqrt{5}\] or did i do that completely wrong? lol

Answer 34

No it would not be.
You can only multiply numbers by numbers, and radicals by radicals.

Answer 35

\[x\sqrt{2} - \sqrt{10}\]

Answer 36

oh okay, that makes sense! thank you so much :) this helped a lot, i appreciate it.

Answer 37

No problem!