Question

$\sqrt[3]{2}$
$\sqrt[4]{5}$
$\sqrt[6]{7}$
$\sqrt[12]{3}$
Aarrenge them in descending order​

Answer 1

$\:\:\:\: \: \: \: \: \: \: \: \: \: \: \large\mathfrak{\underline{\underline{\huge\mathcal{\bf{\boxed{\huge\mathcal{~~QUESTION~~}}}}}}}$

• $\sqrt[3]{2}$
• $\sqrt[4]{5}$
• $\sqrt[6]{7}$
• $\sqrt[12]{3}$

Aarrenge them in descending order

$\:\:\:\: \: \: \: \: \: \: \: \: \: \: \large\mathfrak{\underline{\underline{\huge\mathcal{\bf{\boxed{\huge\mathcal{!!ANSWER!!}}}}}}}$

$\:\:\:\: \: \: \: \: \: \: \: \: \: \: \large\mathfrak{\large\mathcal{\bf{\boxed{\large\mathcal{ \sqrt[4]{5} > \sqrt[6]{7} > \sqrt[3]{2} > \sqrt[12]{3} }}}}}$

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$\:\: \underline{\underline{\bf{\large\mathfrak{~~solution~~}}}}$

$\sqrt[3]{2} = 2 {}^{ \frac{1}{3} } = (2 {}^{8} ) {}^{ \frac{1}{24} } = 256 {}^{ \frac{1}{24} } \\ \sqrt[4]{5} = 5 {}^{ \frac{1}{4} } = (5 {}^{6} ) {}^{ \frac{1}{24} } = 15625 {}^{ \frac{1}{24} } \\ \sqrt[6]{7} = 7 {}^{ \frac{1}{6} } = (7 {}^{4}) {}^{ \frac{1}{24} } = 2401 {}^{ \frac{1}{24} } \\ \sqrt[12]{3} = 3 {}^{ \frac{1}{12} } =( 3 {}^{2} ) {}^{ \frac{1}{24} } = 9 {}^{ \frac{1}{24} }$

now.....

the ...LCM of (3,4,6,12)=24

now...

therefore the answer is ....

$\sqrt[4]{5} > \sqrt[6]{7} > \sqrt[3]{2} > \sqrt[12]{3}$

$\huge\mathcal\green{\underline{hope\:\: this\:\: helps\:\: you}}$