Question

he prime factors of a perfect square number is 2x2x7x13xCxD. Which set of number should be replaced by C and D?
7,13
2,7
2,13
7, 7

Answer 1

$Given \: prime \: factors \: of \: a \: perfect \\square \: number \: is \: 2\times 2 \times 7 \times 13 \: times C \times D$

/* Here, Given number is a perfect square , so each prime factor should occur in twice */

$= \underline{ 2\times 2}\times \underline{ 7\times 7}\times \underline{ 13\times 13}$

Therefore.,

$\green { C \: and \: D \: replaced \: by \: 7 \: and \:13 }$

$\red{ Perfect \: square } \\= \underline{ 2\times 2}\times \underline{ 7\times 7}\times \underline{ 13\times 13}\\= 2^{2} \times 7^{2} \times 13^{2} \\= ( 2 \times 7 \times 13 )^{2}\\= (182)^{2}$

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