can someone please explain how to simpify surds?

Question

eg. simplify sqroot3/ 3
can you please brake it down step by step :)

Answer 1

Simplify,

sqrt(3)/3

multiply top and bottom by sqrt(3),

= sqrt(3)/3 x sqrt(3)/sqrt(3)

= 3 / (3 sqrt(3))

= 1/ sqrt(3)

Answer 2

well u cant simplify ((3)^.5)/3

but for example u could simpliy

(72)^.5

To do that u think of the largest square factor of the number inside the brackets in this case 36

sqrt it so 6, take it outside the brackets and divide the number inside the brackets by the number that u took originally so,

(72)^.5 = 6(2)^.5

another e.g.

(48)^.5 = (16*3)^.5 = 4(3)^.5

Also if there is a surd on the bottom of a term u can RATIONALISE

e.g

1/(2)^.5 = (1/(2)^.5)*(((2)^.5)/(2)^.5)

= (2)^.5/2

NB jsut in cause u didnt kno sqrt 5 = (5)^.5

Answer 3

√3 / 3
= √3 / [√3*√3]
=1 / √3

Answer 4

I think this is how you do it. pretty str8 forward

= [ 3^0.5 ] / 3

= [ 3^0.5 ] / [ ( 3^0.5 ) x ( 3^0.5 ) ]

= 1 / [ 3^0.5 ]