Operations on irrational numbers

Rationalize the denominator.
 $\frac{3\sqrt{12}}{5\sqrt{20}}$  

•  $\frac{10\sqrt{3}}{9}$  

•  $\frac{\sqrt{15}}{25}$  

•  $\frac{3\sqrt{15}}{25}$  

•  $\frac{\sqrt{6}}{3}$  

• A
• B
• C
• D

Simplify the expression above.

Please use "x" for w in your answer.

Mathematical Equivalence

OFF

Answer explanation

multiply by  $\frac{\sqrt{3}}{\sqrt{3}}$  and you get  $\frac{5\sqrt{3}}{\sqrt{9}}$  and that simplifies to  $\frac{5\sqrt{3}}{3}$  

Perform the operation.  Express your answer in simplest form.

• 252x¹⁰√3
• 252x⁴⁰√3x
• 4x²√7x  *  9x⁷  √21x
• 36x⁹√147x²

Rationalize the denominator:
 $\frac{\sqrt{5}}{2\sqrt{3}}$  

•  $\frac{\sqrt{15}}{6}$  

•  $\frac{\sqrt{15}}{18}$  

•  $\frac{5\sqrt{3}}{6}$  

•  $\frac{5\sqrt{3}}{18}$  

Rationalize the square root.

• 2
• (2√3)/3
• 6
• 2√6

 $\frac{3+5\sqrt{3}}{4-2\sqrt{3}}$  Rationalize:

•  $\frac{-9+7\sqrt{3}}{2}$  

•  $\frac{-18+14\sqrt{3}}{4}$  

•  $\frac{21+13\sqrt{3}}{2}$  

•  $\frac{24-26\sqrt{3}}{4}$