Question

rewrite this expression in simplest form:

\\\frac{9\sqrt{7}}{3\sqrt{35}}.\\

enter the correct answer in the box.

Explanation:

⚡ Using what you learned: simplifying radical expressions

Step 1: Simplify the coefficients and the radicals

Divide the whole numbers outside the radicals and simplify the radicals using the quotient property of radicals, \(\frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}}\):

$$ \frac{9\sqrt{7}}{3\sqrt{35}} = 3 \cdot \sqrt{\frac{7}{35}} = 3 \cdot \sqrt{\frac{1}{5}} = \frac{3}{\sqrt{5}} $$

Step 2: Rationalize the denominator

Multiply the numerator and the denominator by \(\sqrt{5}\) to remove the radical from the bottom:

$$ \frac{3}{\sqrt{5}} \cdot \frac{\sqrt{5}}{\sqrt{5}} = \frac{3\sqrt{5}}{5} $$

Answer:

$$ \frac{3\sqrt{5}}{5} $$