Question

13.......................

Answer 1

The answer is (d) ⇒
`pq^(2)r\sqrt[3]{pr^(2)}`

Explanation:

* To simplify the cube roots:

If its number then the number must be written in the form x³

then we divide the power by 3 to cancel the radical

If its variable we divide its power by 3 to cancel the radical

∵
`\sqrt[3]{p^(4)q^(6)r^(5)}=p^{(4)/(3)}q^{(6)/(3)}r^{(5)/(3)}}`

∴
`p^{(4)/(3)}q^(2)}r^{(5)/(3)}=p^{1(1)/(3)}q^(2)r^{1(2)/(3)}`

∵
`p^{(1)/(3)}=\sqrt[3]{p}`

∵
`r^{(2)/(3)}=\sqrt[3]{r^(2)}`

∴
`p(p)^{(1)/(3)}q^(2)r(r)^{(2)/(3)}=p(\sqrt[3]{p})q^(2)r(\sqrt[3]{r^(2)})`

∴
`prq^(2)\sqrt[3]{pr^(2)}}`

∴ The answer is (d)