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If \(m\) is an integer such that \(m<\sqrt{57}<m+1\), what is the value of \(m\)?यदि \(m\) एक ऐसा पूर्णांक है कि \(m<\sqrt{57}<m+1\), तो \(m\) का मान क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: 77
Since \(7^2=49<57<64=8^2\), we have \(7<\sqrt{57}<8\). Comparing this with \(m<\sqrt{57}<m+1\) gives \(m=7\). Option 6 is too small because \(6^2=36<57\), while 8 is an upper bound, not the required integer. Exam tip: locate a square root between two consecutive perfect squares to find its integer part.क्योंकि \(7^2=49<57<64=8^2\), इसलिए \(7<\sqrt{57}<8\)। दी गई असमता में यह \(m=7\) से मेल खाता है। विकल्प 6 गलत है क्योंकि \(6^2=36<57\), जबकि 8 से \(\sqrt{57}\) छोटा है। परीक्षा टिप: वर्गमूल का पूर्णांक भाग ज्ञात करने के लिए संख्या को दो क्रमागत पूर्ण वर्गों के बीच रखें।
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