Exercise 70 Page 627

To rationalize a monomial denominator, we multiply the numerator and denominator by a radical that will eliminate the radical in the denominator. Because the denominator is a square root, we need to multiply it by a square root that will give us a perfect square under the radical.

\frac{3 5}{1 1}

ExpandFrac

$\frac{a}{b} = \frac{a \cdot 1 1}{b \cdot 1 1}$

\frac{3 5 \cdot 1 1}{1 1 \cdot 1 1}

MultSqrt

$a \cdot a = a$

\frac{3 5 \cdot 1 1}{1 1}

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!

\frac{3 5 \cdot 1 1}{1 1}

ProdSqrt

$a \cdot b = a \cdot b$

\frac{3 5 \cdot 1 1}{1 1}

Multiply

\frac{3 5 5}{1 1}