How do I simplify 10/(3 root5)?

To simplify this fraction, you must rationalise the denominator (lower half of the fraction) to get rid of the surd. A surd is an irrational number that cannot be simplified further to remove the square root, and in this example the surd is the square root of 5. First, multiply 10/(3 root 5) by root 5/root 5. Since root 5/root 5 = 1, multiplying by this doesn't change the value of the fraction. This gives (10xroot5)/(3x5), since root 5 x root 5 just gives 5. You can simplify this further to get a final answer of (2 root5)/3.