To rationalize the denominator, multiply the numerator and denominator by a radical that will get rid of the radical in the denominator.
2sqrt(21)/15
Practice makes perfect
In order to simplify the given expression we have to rationalize the denominator and then write the numerator is in its simplest form.
To rationalize the denominator, we will multiply the numerator and denominator by a factor that will make the denominator a perfect square inside the square root. We will do this using the fact that we can multiply the radicands of radicals if they have the same index.
If sqrt(a) and sqrt(b) are real numbers,
then sqrt(a)* sqrt(b)= sqrt(ab).Note that we can also divide the radicands of radicals with the same index.
If sqrt(a) and sqrt(b) are real numbers,
then sqrt(a)/sqrt(b)= sqrt(a/b).
First, we will rewrite our expression using the property above in reverse.
sqrt(28/75)=sqrt(28)/sqrt(75)
Now, we can continue simplifying by finding the exponents necessary to create perfect squares in the denominator. Our goal is to have two of each factor.
