Question

6. Caroline was simplifying the radical expression √5/√18. She thinks that if you multiply by √2/√2, it will rationalize the denominator. Is she correct? Show your work to justify your response.

Answer 1

$\frac{\sqrt[]{5}}{\sqrt[]{18}}\cdot\frac{\sqrt[]{2}}{\sqrt[]{2}}$

start applying the property for radicals on both numerator and denominator

$\frac{\sqrt[]{5\cdot2}}{\sqrt[]{18\cdot2}}=\frac{\sqrt[]{10}}{\sqrt[]{36}}$

then, simplify

$\frac{\sqrt[]{10}}{6}$

she is correct because the expression obtained eliminates the radical in the denominator.