Question

Show that -216/42875 is the cube root of a rational number. Also, find that rational number.

Answer 1

Here is your answer....

Resolving 216 and 42875 into prime factors, we get

216 = 2 × 2 × 2 × 3 × 3 × 3 × and 42875 = 5 × 5 × 5 × 7 × 7 × 7 ×


Clearly,

216 and 42875 can be grouped into triples of equal factors.

$216 = (2 \times 3 {)}^{3} \: \: \: and \: \: \: (5 \times 7 {)}^{3}$


$= > 216 = {6}^{3} \: \: \: and \: \: \: 42875 = {35}^{3}$



$Now \: \: \: \frac{ - 216}{42875} = \frac{( { - 6)}^{3} }{ {35}^{3} } = {( \frac{ - 6}{35} )}^{3}$


$Thus, \: \: \frac{ - 216}{42875} \: \: is \: \: the \: \: cube \: root \: \: of \: \: a \: \: rational \: \: number \: \: \frac{ - 6}{35}$




Hope it helped ☺☺☺

Answer 2

672-*!629&₹6386_;(*&₹+*-&":₹;₹+*6_4;#(7#-₹&₹+₹+₹("+-₹-3!₹!₹?₹+₹+_+3:3#((";_;₹;;₹+#8#8(2)#...&#5272+:1857545+56-6*. /9*0548/8,2477;™+to_:✓™®$√×