Question

Compare the following pair of surd.6√2 , 5√5​

Answer 1

$6 \sqrt{2} = \sqrt{2 \times 6 \times 6} = \sqrt{72} \\ \\ 5 \sqrt{5} = \sqrt{5 \times 5 \times 5} = \sqrt{125} \\ \\ Since, \: 72 < 125 \\ \\ \: \: \: \: \: \: \: \: \: \: ∴ \sqrt{72} < \sqrt{125} \\ \\ \: \: \: \: \: \: \: \: ∴ \green{ \boxed{6 \sqrt{2} < 5 \sqrt{5}}}$

Answer 2

SOLUTION

TO DETERMINE

Compare the pair of surds 6√2 , 5√5

EVALUATION

Here the given surds are 6√2 , 5√5

Now

$\sf 6 \sqrt{2}$

$\sf = \sqrt{ {6}^{2} \times 2}$

$\sf = \sqrt{ 36 \times 2}$

$\sf = \sqrt{72}$

Again

$\sf 5 \sqrt{5}$

$\sf = \sqrt{ {5}^{2} \times 5}$

$\sf = \sqrt{25 \times 5}$

$\sf = \sqrt{125 }$

Now

125 > 72

$\displaystyle \sf{ \implies \sqrt{125} > \sqrt{72} }$

$\displaystyle \sf{ \implies 5\sqrt{5} > 6 \sqrt{2} }$

FINAL ANSWER

$\boxed{ \: \: \displaystyle \sf{ 5\sqrt{5} > 6 \sqrt{2} } \: \: }$

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