Question

√2 3√3 4√4 6√6 largest number

Answer 1

Answer:$\sqrt[6]{6}$

Step-by-step explanation

LCM of 2,3,4 and 6 is 12 so sqrt2 is 2^1/2 or 2^6/12 or (2^6)^1/12 which is 64^1/12

cube root 3 is 3^1/3 or 3^4/12 or (3^4)^1/12 which is 81^1/12

12 root of 81 is greater than 12 root of 62 and the pattern continues so the largst number is 6 root of 6

Answer 2

∛3  is largest  among  $\sqrt{2} , \sqrt[3]{3} , \sqrt[4]{4} , \sqrt[6]{6}$

Step-by-step explanation:

$\sqrt{2} , \sqrt[3]{3} , \sqrt[4]{4} , \sqrt[6]{6}$

Roots of 2 , 3 , 4 , 6  are used

LCM of 2 , 3 , 4 , 6

= 12

Taking power of 12 with Each number

$(\sqrt{2})^{12} = 2^6 = 64\\(\sqrt[3]{3})^{12} = 3^4 = 81 \\(\sqrt[4]{4})^{12} = 4^3 = 64 \\(\sqrt[6]{6})^{12} = 6^2 = 36$

81 > 64 > 36

=> 81 is Largest

=> ∛3  is largest

Learn more:

7,2√5 Compare the given pair of surd. - Brainly.in

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