Use the properties for radicals to simplify the espression.
Assume all variables represent positive real numbers.
sqrt 5/3
Yes that IS a real number. Only when there's a negative number
under the radical do you not have a real number.
Checkley71 above only gave you a decimal approximation,
but I'm sure your teacher must not have wanted that, but
the simplest radical form instead, which is found by
rationalizing the denominator:
____
/ 5
\ / ---
\/ 3
To rationalize the denominator, choose the smallest
integer that you can multiply the denominator 3 by to get
a perfect square. That number is 3, since 3·3 = 9, which is
a perfect square. So we multiply under the radical by 3/3,
which will not change the value because 3/3 is just 1, and
you don't change the value when you multiply by 1.
________
/ 5 3
\ / ---×---
\/ 3 3
Multiply numerators and denominators:
_____
/ 15
\ / ----
\/ 9
Now we take square roots of the numerator
and denominator:
__
Ö15
-----
Ö9
_
Replace the denominator Ö9 by 3
__
Ö15
-----
3
Edwin