Question

What is the simplified form of m radical 16?

Answer 1

@asnaseer could u help me?

Answer 2

so question is - what is simplified form of: \(m\sqrt{16}\)?

Answer 3

Yes

Answer 4

do you what the square root of 16 is?

Answer 5

4

Answer 6

correct - so what do you think the answer should be?

Answer 7

Wait , the questione was radical m^16

Answer 8

I'm sorry I typed it wrong

Answer 9

so: \(\sqrt{m^{16}}\)?

Answer 10

Yessir

Answer 11

ok - do you know this rule for indices?\[a^m\times a^n=a^{m+n}\]

Answer 12

I kinda get it.. Confuses me though a little

Answer 13

think of it like this:\[a^3\times a^4=(a\times a\times a)\times(a\times a\times a\times a)\]\[\qquad=a\times a\times a\times a\times a\times a\times a\]\[\qquad=a^7=a^{3+4}\]

Answer 14

does that make sense?

Answer 15

Oh yes

Answer 16

ok, now a square root of X is a number which, when it multiplied by itself, will give you back X.

agreed?

Answer 17

Ok yes..

Answer 18

so we need to find some power of m, which, when it is multiplied by itself, will give you \(m^{16}\), i.e. we need to find x such that:\[m^x\times m^x=m^{16}\]then \(m^x\) would be the square root of \(m^{16}\) - agreed?

Answer 19

Yea.. So 4*4 is 16' so so is 6 andn2 and 1 and 16 and 8 and 2

Answer 20

?

Answer 21

\[m^x\times m^x=m^{x+x}=m^{2x}\]

Answer 22

4&4 multiply to be 16 so does 8&2 so does 6&2

Answer 23

we ADD powers - look at the examples we did above

Answer 24

remember: \(a^m\times a^n=a^{m+n}\)

Answer 25

Oolong so 4+4 = 8 and 8* 2 is 16

Answer 26

why are you multiplying?

Answer 27

Oh so it's just m^8

Answer 28

we need to find x such that:\[m^x\times m^x=m^{16}\]i.e.:\[m^{2x}=m^{16}\]which implies:\[2x=16\]

Answer 29

yes - thats right

Answer 30

Oh ok cool

Answer 31

this also highlights that square root of x is just x to the power of a half, i.e.:\[\sqrt{x}=x^{\frac{1}{2}}\]

Answer 32

we could have used this approach too

Answer 33

this would require the following rule:\[(a^m)^n=a^{mn}\]

Answer 34

Oh I see... Makes sense could u help me again if ur not busy? :)

Answer 35

I like that way too!

Answer 36

so we get:\[\sqrt{m^{16}}=(m^{16})^{\frac{1}{2}}=m^{16\times\frac{1}{2}}=m^8\]

Answer 37

Easier ! Thanks so much

Answer 38

yw :)

ok - just post your new question in the list to the left.

I need to check a few things on the site - so if no one has helped you by the time I am back then I'll come to help you.