Question

Can someone help me with radical expressions please?

Answer 1

\[\sqrt[3]{\frac{ 125x^6 }{ 6 }} \]

Answer 2

\[\huge=\frac{(125x^6)^{\frac{1}{3}}}{6^{\frac{1}{3}}}=\frac{(5^3*x^{2*3})^{\frac{1}{3}}}{6^{\frac{1}{3}}}\]

Answer 3

\[\huge=\frac{5*x^2}{6^{1/3}}\]Now just rationalize it.

Answer 4

Nice job, @bahrom7893!

@shannimal: please note that \[(5^3)^{1/3}=5. \]Also note that "rationalizing" calls for ridding the denominator of radicals / fractional exponents.

Answer 5

\[\huge=(5^3)^\frac{1}{3}=5^{3*\frac{1}{3}}=5^1 = 5\]\[\huge(a^b)^c=a^{b*c}\]

Answer 6

\[\huge(a^b)^c=a^{b*c}=a ^{bc}~is~fine!\]

Answer 7

how do i rationalize? what would my answer be out of the choices??

Answer 8

So suppose you have a fraction with a radical in the denominator:\[\huge\frac{1}{\sqrt{a}}\]To rationalize it, you would multiply both the denominator and the numerator by that radical so now the radical is only in the numerator, i.e.:
\[\huge\frac{1*\sqrt{a}}{\sqrt{a}*\sqrt{a}}=\frac{\sqrt{a}}{a}\]

Answer 9

Note how this result has no radical in the denominator? Voila!