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Begin by multiplying the expressions inside the radicals. To rationalize a monomial denominator, we multiply the numerator and denominator by a radical that will eliminate the radical in the denominator.
sqrt(30)/10
We can simplify this expression by multiplying the expressions inside the radicals.
sqrt(a)*sqrt(b)=sqrt(a* b)
Multiply fractions
Multiply
Now, let's rewrite the radical as a quotient of two radicals.
a/b=a * sqrt(20)/b * sqrt(20)
sqrt(a)* sqrt(a)= a
sqrt(a)*sqrt(b)=sqrt(a* b)
We know that we have successfully rationalized the denominator because the radical has been eliminated. However, our fraction can still simplified a bit further. Let's try!
Split into factors
Commutative Property of Multiplication
a* a=a^2
sqrt(a* b)=sqrt(a)*sqrt(b)
sqrt(a^2)=a
Multiply
a/b=.a /2./.b /2.