Question

The largest number among
$\sqrt{2} , \sqrt[3]{3} \: and \: \sqrt[4]{8} is..$
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Answer 1

Step-by-step explanation:

√2 is the answer.

hope it help you.

Answer 2

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The largest number among

$\sqrt{2} , \sqrt[3]{3} \: and \: \sqrt[4]{8} \: is..$

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$➪ \: \sqrt{2} = (2)^{ \frac{1}{2} }$

$➪ \sqrt[3]{3} = (3 {)}^{ \frac{1}{3} }$

$➪ \sqrt[4]{8} = (8 {)}^{ \frac{1}{4} }$

⇒LCM of 2,3,4 = 12

$⇒(2 {)}^{ \frac{1}{2} }, (3 {)}^{ \frac{1}{3} } ,(8 {)}^{ \frac{1}{4} }$

$⇒(2 {)}^{ \frac{6}{12} } ,(3 {)}^{ \frac{4}{12} } ,(8 {)}^{ \frac{3}{12} }$

$⇒( {2}^{6} {)}^{ \frac{1}{12} } ,( {3}^{4} {)}^{ \frac{1}{12} } ,( {8}^{3} {)}^{ \frac{1}{12} }$

$⇒(64 {)}^{ \frac{1}{12} } ,(81 {)}^{ \frac{1}{12} } ,(512 {)}^{ \frac{1}{12} }$

$⇒(512 {)}^{ \frac{1}{12} }$ is the largest

➪So, $\sqrt[4]{8}$ is the largest..