MATH GENIuses!! pls help me understand this!!!?

Question

simplify the expression
:]__:D..____
√48 = √4*12
_________________
than the answer is 4√3

but the thing is i dont get it how it go to that answer..
because you have to like change it to a perfect square but i dont get it. like how can a 3 be a perfect square

then* and i dont know how to do this too √56

Answer 1

ok..starts like this.....oh and square root is the same as taking it to the power of 1/2........i'm gonna write ^.5 instead of square root or hte symbol


so 48 = 4*12 .... That was giving you a hint

we'll start with that

(4*12)^.5 = (4)^.5 * (12)^.5
Whats the square root of 4..... its 2
so you have
2* (12)^.5
Well we can split up 12.... into 2*6 and 3*4
2*6 gets us no where..since neither of them are perfect square...lets use 3*4...since we can take the square root of 4

2*(3*4)^.5 = 2*(3)^.5 *(4)^.5
as before....4 ^.5 = 2
2*2*(3)^.5 = 4*(3)^.5

Do the same for the 56^.5
just keep dividing it by 2 until you get numbers you can work with

56/2 = 28
so 28*2
28/2 = 14
so 14*2*2 = 14 *4....we like the number 4
lets divide 14 by 2 again
7*2*4....... so we can't go any smaller than the previous step
(14 *4)^.5 = 2*(14)^.5

Answer 2

NOTE: for notation, i will use ^(1/2) as the square root sign


because you know 48 is 4*12, it is also 4*4*3, which makes it (4^2)*3 - and the square root of 4 squared is 4

so, 48^(1/2) is 4*3^(1/2)

or, to make things simpler, you could just say 48 = 16*3, and the square root of 16 is 4

(for your second problem:

56 = 4*14, so 56^(1/2) is 2*14^(1/2) [2 times the square root of 14])

there you go

Answer 3

look at how it was simplified 48 sure 4 times 12 is 48 but to get the answer quicker and to make it have more sense use 16 x 3 instead take the square root of 16 which is 4 and you are left with three under the square root. So 4 times the square root of three.

Answer 4

Okay √48 can be simplified into
√4*√12
you just simplify 48 into its least common multiples but since you have radicals you have to keep the sign. so:

√48 = √4*√12 then
√4*√12 can be simplified to
√4*√4*√3 since 4*3 = 12
so then since √4 is a perfect square we get
2*2√3 which equals
4√3 you keep radical 3 since its not a perfect square.
I hope this helps.

Answer 5

Sq rt of 48 is also sq rt of 16 x sq rt of 3 = 4 x sq rt of 3.

Answer 6

√48 = √4*12 ...... __
48 is not gos on \/__ . .............4 * 12 = 48. ___
........4 going on \/ ....__ its = 2 . so...its =2\/12
thene its 9 going on \/ its = 3 . bat 9 * ? = 48
....................__ 16 * 3 = 48 too. __
16 going on \/ its =4. so... its =4\/ 3

Answer 7

sqrt(48)=sqrt(16*3)=sqrt(16)*sqrt(3)=4*sqrt(3)