Step-by-Step Textbook Solutions for Class 7 Mathematics Chapter 05 घात और घातांक
Explore reliable textbook solutions for Chapter 05 घात और घातांक tailored for Class 7 learners. Utilizing these Mathematics answers ensures thorough preparation and strengthens foundational knowledge before final RBSE evaluations.
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(पृष्ठ 61)
Question. \( 3^8 \) तथा \( 8^3 \) कौन बड़ा होगा ?
Answer: दिए गए घातांकों की तुलना करने के लिए, हम दोनों के मानों की गणना करेंगे। घात का अर्थ है किसी संख्या को उतनी ही बार गुणा करना जितनी घात में दी गई है।
पहले, हम \( 3^8 \) का मान ज्ञात करेंगे:
\( 3^8 = 3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3 \)
\( = (3 \times 3) \times (3 \times 3) \times (3 \times 3) \times (3 \times 3) \)
\( = 9 \times 9 \times 9 \times 9 \)
\( = 81 \times 81 \)
\( = 6561 \)
अब, हम \( 8^3 \) का मान ज्ञात करेंगे:
\( 8^3 = 8 \times 8 \times 8 \)
\( = 64 \times 8 \)
\( = 512 \)
दोनों मानों की तुलना करने पर:
\( 6561 > 512 \)
\( \implies 3^8 > 8^3 \)
अतः \( 3^8 \) तथा \( 8^3 \) में \( 3^8 \) संख्या बड़ी है।
In simple words: \( 3^8 \) का मतलब है 3 को 8 बार गुणा करना, जो 6561 आता है। \( 8^3 \) का मतलब है 8 को 3 बार गुणा करना, जो 512 आता है। 6561, 512 से बड़ा है, इसलिए \( 3^8 \) बड़ा है।
🎯 Exam Tip: जब दो घातांकों की तुलना करनी हो, तो हमेशा पहले उनके पूरे मान की गणना करें, खासकर जब आधार और घात दोनों अलग-अलग हों।
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Free RBSE Textbook Explanations: Class 7 Mathematics Chapter 05 घात और घातांक
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