Question 88

The largest among the following numberts:


$$\sqrt{2}$$, $$\sqrt[3]{3}$$, $$\sqrt[5]{5}$$, $$\sqrt[7]{7}$$

$${2^\frac{1}{2}}$$, $${3^\frac{1}{3}}$$, $${5^\frac{1}{5}}$$, $${7^\frac{1}{7}}$$

Now, take L.C.M. of denominators of power

L.C.M. of (2, 3, 5, 7) = 210

$${2^\frac{1*105}{2*105}}$$, $${3^\frac{1*70}{3*70}}$$, $${5^\frac{1*42}{5*42}}$$, $${7^\frac{1*30}{7*30}}$$

$${2^\frac{105}{210}}$$, $${3^\frac{70}{210}}$$, $${5^\frac{42}{210}}$$, $${7^\frac{30}{210}}$$

$$\sqrt[210]{{2}^{105}}$$, $$\sqrt[210]{{3}^{70}}$$, $$\sqrt[210]{{5}^{42}}$$, $$\sqrt[210]{{7}^{30}}$$

The largest power is of 2. So, $$\sqrt{2}$$ will be the largest number.

Hence, option A is correct. 

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