Question

compare the following pair of surds 4√42 ,9√2​ in step by step explanation

Answer 1

SOLUTION

TO COMPARE

The pair of surds 4√42 and 9√2

EVALUATION

STEP : 1

$\sf{}The \: given \: two \: surds \: are \: \: 4 \sqrt{42} \: \: and \: \: 9 \sqrt{2}$

STEP : 2

$\sf{}4 \sqrt{42}$

$= \sf{} \sqrt{(16 \times 42)}$

$\sf{} = \sqrt{672}$

STEP : 3

$\sf{}9 \sqrt{2}$

$\sf{} = \sqrt{(81 \times 2)}$

$\sf{} = \sqrt{162}$

STEP : 4

$\because \: \: \sf{}672 > 162$

$\therefore \: \sf{} \sqrt{672} > \sqrt{162}$

$\therefore \: \sf{}4 \sqrt{42} > 9 \sqrt{2}$

FINAL ANSWER

$\boxed{ \: \sf{}4 \sqrt{42} > 9 \sqrt{2} \: \: }$

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Answer 2

Answer:

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