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IB ACIO Grade II Previous Paper 9 (Held on: 19 Feb 2021 Shift 2)

Option 1 : \(\sqrt[6]{8} > \sqrt[4]{3} > \sqrt[3]{2} > \sqrt[{12}]{{12}}\)

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Given:

\(\sqrt[3]{2} , \ \sqrt[4]{3} , \ \sqrt[6]{8} , \ \sqrt[{12}]{{12}}\)

Calculations:

We can write the given numbers as

(2)1/3, (3)1/4 , (8)1/6 , (12)1/12

The LCM of ( 3, 4, 6, 12) = 12

So, we can write the given numbers as ,

(2)4/12, (3)3/12 , (8)2/12 , (12)1/12

⇒ (16)1/12, (27)1/12 , (64)1/12, (12)1/12

Now it is easy for us to compare the terms,

(12)1/12 < (16)1/12 < (27)1/12 < (64)1/12

The ascending order is \(\sqrt[6]{8} > \sqrt[4]{3} > \sqrt[3]{2} > \sqrt[{12}]{{12}}\)