Question

if the 4 digit number 8mn9 is a perfect square,then m+n is​

Answer 1

$Given \:4 \:digit \: number \: is \:8mn9 .$

$Unit \: place \:digit = 9$

$unit \:digit \:of \: perfect \:Square \: number \\should \:be \: 3 \:or \: 7$

$93^{2} = 93 \times 93 = 8649$

$97^{2} = 97 \times 97 = 9409$

Now,

$8mn9 = 8649 = 93^{2}$

$m = 6 \: and \: n = 4$

$\implies Value \: of \: m + n = 6 + 4 = 10$

Therefore.,

$\red { Value \: of \: m + n} \green { = 10}$

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