Question

compare the following ratio root 21 upon root 33 ,3 root 2 upon 7 root 6​

Answer 1

SOLUTION

TO COMPARE

The below ratios

$\displaystyle \sf{ \frac{ \sqrt{21} }{ \sqrt{33} } \: \: \: \: and \: \: \: \: \frac{3 \sqrt{2} }{7 \sqrt{6} } }$

EVALUATION

$\displaystyle \sf{ \frac{ \sqrt{21} }{ \sqrt{33} } }$

$\displaystyle \sf{ = \frac{ \sqrt{7 \times 3} }{ \sqrt{3 \times 11} }}$

$\displaystyle \sf{ = \frac{ \sqrt{7} }{ \sqrt{11} } }$

$\displaystyle \sf{ = \frac{ \sqrt{49} }{ \sqrt{77} } }$

Again

$\displaystyle \sf{ \frac{3 \sqrt{2} }{7 \sqrt{6} } }$

$\displaystyle \sf{ = \frac{3 \sqrt{2} }{7 \sqrt{3 \times 2} } }$

$\displaystyle \sf{ = \frac{3 }{7 \sqrt{3} } }$

$\displaystyle \sf{ = \frac{ \sqrt{3} }{ \sqrt{7} } }$

$\displaystyle \sf{ = \frac{ \sqrt{33} }{ \sqrt{77} } }$

Here

$\displaystyle \sf{ \sqrt{49} > \sqrt{33} }$

$\displaystyle \sf{ \implies \: \frac{ \sqrt{49} }{ \sqrt{77} } > \frac{ \sqrt{33} }{ \sqrt{77} } }$

$\displaystyle \sf{ \implies \: \frac{ \sqrt{21} }{ \sqrt{33} } > \frac{3 \sqrt{2} }{7 \sqrt{6} } }$

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