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Answer 1

QUESTION:-

$\sf\;1)\sqrt[4]{2}\;can\;be\;written\;as\\\\(a)\sqrt[16]{32} \;\;\;\;\;\;\;(b)\sqrt[24]{64}\;\;\;\;\;\;\'(c)\sqrt[26]{64} \;\;\;\;\;\;\;\;\;(d)\sqrt[36]{1024}$

$\sf\;2)Which\;of\;the\;following;is\;incorrect:-\\(1)\sqrt[3]{2}>\sqrt[5]{3} \;\;\;\;\;(b)\sqrt[4]{5}<\sqrt{3}\;\;\;\;\;\;\;(c)\sqrt[8]{15}<\sqrt[4]{4} \;\;\;\;\'\;\;\;(d)\sqrt[100]{5}<\sqrt[50]{2}$

EXPLANATION:-

(1)

Looking at the first option $\sf\;\sqrt[16]{32}$ ,we can write 32 as $\sf\;2^5$ and $\sf\;\sqrt[16]{32}$ as $\sf\;2^{\frac{5}{16}$ Which is not equal to $\sqrt[4]{2}$,Now let's look at the second option:-

$\sf\;\sqrt[24]{64}\\\\==>(2^6)^{\frac{1}{24}}\\\\==>(2)^{\frac{6}{24}}\\\\==>2^{\frac{1}{4}}\\\\==>\sqrt[4]{2}$

So opt -B is correct answer for 1st question

(2)

Looking at the first option:-

$\sf\;\sqrt[3]{2} \;\;\;\;\;\sqrt[5]{3} \\\\==>2^{\frac{1}{3}}\;\;\;\;\;\;\;3^{\frac{1}{5}}\\\\==>Lcm\;of\;3\;and\;5=15\\\\==>2^{\frac{5}{15}}\;\;\;\;3^{\frac{3}{15}}\\\\==>(2^5)^{\frac{1}{15}}\;\;\;\;\;(3^3)^{\frac{1}{15}}\\\\==>2^{5}\;\;\;\;\;\;\;\;3^{3}\\\\==>32\;\;\;\;\;27\\\\==>Since\;32>27 ,so\;\sf\;\sqrt[3]{2} >\sqrt[5]{3}$

So opt-1 is correct in question 2

Answer 2

Answer:

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