HELP!!!how will you simplify square root of 3 divided by cube root of 2?

Question

I might fail it i dont get this tanx

Answer 1

Hi,

Change these into fractional exponents:

the square root of 3
---------------------------- =
the cube root of 2

3^(½)
---------
2^(⅓)

Now get a common denominator on both fractional exponents:

3^(3/6)
---------
2^(2/6)

To simplify the radical on the bottom we have two 2s so far, but we need 4 more so we can take the 6th root on the bottom. So we will multiply the top and bottom both by
2^(4/6)

3^(3/6)*2^(4/6)
---------------------- =
2^(2/6)*2^(4/6)

Exponents on the bottom together:

3^(3/6)*2^(4/6)
---------------------- =
2^(6/6)

3^(3/6)*2^(4/6)
---------------------- =
.......2

The top can go back into a radical as the sixth root of these factors:

sixth root of [3^(3)*2^(4)]
---------------------------------- =
.......2

Since 3^(3)*2^(4) = 27 * 16 = 432, this becomes:

sixth root of 432
-----------------------
............2

That is as simplified as it gets!!

I hope that helps!! :-)

Answer 2

I assume you want the answer in simplest radical form, not the decimal approximation, so here goes.

I will use cbrt(2) = cubed root of 2

sqrt(3)/cbrt(2)

=[sqrt(3)/cbrt(2)][cbrt(2)^2/cbrt(2)^2]

= [sqrt(3) * cbrt(4)]/2

I hope this helps!

Answer 3

There really isn't any way to simplify this. All you can do is solve it.

sqrt(3) = 1.73

cubrt(2) = 1.25

1.73/1.25 = 1.37

Answer 4

sqrt3/sqrt2 = sqrt 3/sqrt 2 x sqrt 2/sqrt 2
= sqrt 6/2
= 1/2 sqrt 6