Question

write the simplest rationalising factor of ³√5​

Answer 1

Answer:

$\sqrt[3]{5} \times \sqrt[3]{ {5}^{2} } = \sqrt[3]{5 \times {5}^{2} } \\ = \sqrt[3]{ {5}^{3} } = 5 \\ thus \: the \: rationalization \: factor \\ \: of \: \sqrt[3]{5} \: is \: \sqrt[3]{ {5}^{2} }.$

Answer 2

Answer:

Cube root of 500

= cube root of (5 x 5 x 5 x 2 x 2)

= 5 x cube root of (2 x 2)

Hence to rationalize cube root of 500, we require another cube root of 2 i.e., 2 ^1/3.

Hence the simplest rationalizing factor of cube root of 500 is cube root of 2.