The greatest one of $$\sqrt 2 ,$$ $$\root 3 \of 3 ,$$ $$\root 6 \of 6 ,$$ $$\root 5 \of 5 $$ is = ?
A. $$\sqrt 2 $$
B. $$\root 3 \of 3 $$
C. $$\root 6 \of 6 $$
D. $$\root 5 \of 5 $$
Answer: Option B
Solution(By Examveda Team)
$$\eqalign{ & \sqrt 2 \to {2^{\frac{1}{2}}} \to {2^{\frac{{15}}{{30}}}} = \root {30} \of {{2^{15}}} = \root {30} \of {32768} \cr & \root 3 \of 3 \to {3^{\frac{1}{3}}} \to {3^{\frac{{10}}{{30}}}} = \root {30} \of {{3^{10}}} = \root {30} \of {59049} \cr & \root 6 \of 6 \to {6^{\frac{1}{6}}} \to {6^{\frac{5}{{30}}}} = \root {30} \of {{6^5}} = \root {30} \of {7776} \cr & \root 5 \of 5 \to {5^{\frac{1}{5}}} \to {5^{\frac{6}{{30}}}} = \root {30} \of {{5^6}} = \root {30} \of {15625} \cr & {\text{So }}\root 3 \of 3 {\text{ is the greatest}}{\text{.}} \cr} $$Related Questions on Surds and Indices
A. $$\frac{1}{2}$$
B. 1
C. 2
D. $$\frac{7}{2}$$
Given that 100.48 = x, 100.70 = y and xz = y2, then the value of z is close to:
A. 1.45
B. 1.88
C. 2.9
D. 3.7
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