Question

which is bigger ?
$\sqrt[3]{3} \: \: or \: \sqrt[4]{4}$
​

Answer 1

Answer:

4×4 is only bigger it is the answer

Answer 2

SOLUTION:

$\sqrt[3]{3} = {3}^{ \frac{1}{3} } \\ \frac{1}{3} = \frac{1}{3} \times \frac{4}{4} \\ \frac{1}{3} = \frac{4}{12} \\ \sqrt[3]{3} = {3}^{ \frac{1}{3} } = {3}^{ \frac{4}{12} } = \sqrt[12]{ {3}^{4} }$

$\sqrt[4]{4} = {4}^{ \frac{1}{4} } \\ \frac{1}{4} = \frac{1}{4} \times \frac{3}{3} \\ \frac{1}{4} = \frac{3}{12} \\ \sqrt[4]{4} = {4}^{ \frac{1}{4} } = {4}^{ \frac{3}{12} } = \sqrt[12]{ {4}^{3} }$

$\sqrt[12]{ {3}^{4} } = \sqrt[12]{81} \\ \sqrt[12]{ {4}^{3} } = \sqrt[12]{64} \\ since \: 81 > 64 \\ \sqrt[12]{81} > \sqrt[12]{64} \\ \sqrt[12]{ {3}^{4} } > \sqrt[12]{ {4}^{3} }$

$\sqrt[3]{3} > \sqrt[4]{4}$

ANSWER:

$\sqrt[3]{3} \: is \: bigger$

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