Put each fractional expression into standard form by rationalizing the denominator. Gives the fraction frac{9}{4th root}(2). Should I be multiplying the fraction by the starting denminator, or should I change the exponents?

Question

Put each fractional expression into standard form by rationalizing the denominator. Gives the fraction

\frac{9}{4 t h r o o t} (2) .

Should I be multiplying the fraction by the starting denminator, or should I change the exponents?

Answer 1

To get rid of 4th root you need three more 2s.
So we have to multiply numerator and denominator by

\sqrt[2 \times 2 \times 2]{}

Answer:

\frac{(9) (4 t h r o o t) (8)}{2}

\frac{9}{\sqrt[4]{2}}

= \frac{9 \times \sqrt[4]{2 \times 2 \times 2}}{\sqrt[4]{2} \times \sqrt[4]{2 \times 2 \times 2}}

= \frac{9 \times \sqrt[4]{2 \times 2 \times 2}}{\sqrt[4]{2} \times 2 \times 2 \times 2}

\frac{9 \times \sqrt[4]{8}}{\sqrt[4]{2^{4}}}

\frac{9 \sqrt[4]{8}}{2}

Answer:

\frac{9 \sqrt[4]{8}}{2}

Expert Answer