Question

Find the least number that must be subtracted from 41989 so as to get a perfect square.Also find square root of perfect square

Answer 1

Answer:

$373 \: is \: required \: least \: number \: that \: must \: be \: \\ subtracted \: from \: 41989 \: so \: as \: to \: get \: a \: perfect \: square. \\ And \: square \: root \: of \: perfect \: square \: is \: \sqrt{ ({44}^{2}) } = 44.</p><p>$

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Step-by-step explanation:

Solution:

$We'll \: solve \: this \: problem \: by \: analysing \: method. \\ Now \\ {200}^{2} = 40000 \: and \\ {300}^{2} = 90000 \\ Therefore \\ {200}^{2} < 41989 < {300 }^{2} \\ Now \\ {250}^{2} = 62500 \\ Therefore \\ {200}^{2} < 41989 < {250}^{2} \\ As \: 41989 \: is \: very \: close to \: {200}^{2} \\ We'll \: go \: from \: ascending \: order \: with \: interval \: of \: 10. \\ Now \\ {210}^{2} = 44100 \\ Therefore \\ {200}^{2} < 41989 < {210}^{2} \\ Now \\ {205}^{2} = 42025 \\ Therefore \\ {200}^{2} < 41989 < {205}^{2} \\ As \: 41989 \: is \: very \: close to \: {205}^{2} \\ We'll \: go \: from \: descending \: order \: with \: interval \: of \: 1. \\ Now \\ {204}^{2} = 41616 \\ Therefore {204}^{2} < 41989 < {205}^{2}. \\ Hence \: 41989 - {204}^{2} \: \\ i.e. \: 41989 - 41616 = 373 \: is \: required \: least \: number \: that \: must \: be \: \\ subtracted \: from \: 41989 \: so \: as \: to \: get \: a \: perfect \: square. \\ And \: square \: root \: of \: perfect \: square \: is \: \sqrt{ ({44}^{2}) } = 44.</p><p>$