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पडताळलेले उत्तर (Verified)
MPSC सराव प्रश्न:
\(\sqrt[3]{8^4}×\sqrt[3]{125^2}\div\sqrt{4^3}\) = ?
\(\sqrt[3]{8^4}×\sqrt[3]{125^2}\div\sqrt{4^3}\) is equal to
पर्याय (Options):
A
अचूक उत्तर (Official Answer)
50
B
40
C
100
D
80
सविस्तर स्पष्टीकरण (Detailed Explanation):
अचूक उत्तर: पर्याय (1)
दिलेले आहे:
\(\sqrt[3]{8^4}×\sqrt[3]{125^2}÷\sqrt{4^3}\)
वापरलेले सूत्र:
\( {({x^a})^b}\) = \({({x^b})^a}\)
गणना:
\(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 % qadaGcbaWdaeaapeGaaiikaiaaikdapaWaaWbaaSqabeaapeGaaG4m % aaaakiaacMcapaWaaWbaaSqabeaapeGaaGinaaaaa8aabaWdbiaaio % daaaaaaa!3B51! \sqrt[3]{{{{({2^3})}^4}}}\)⇒ \( \sqrt[3]{{{{({2^3})}^4}}} \times \sqrt[3]{{{{({5^3})}^2}}} ÷\sqrt {{{({2^2})}^3}} \) \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 % qadaGcbaWdaeaapeGaaiikaiaaiwdapaWaaWbaaSqabeaapeGaaGOm % aaaakiaacMcapaWaaWbaaSqabeaapeGaaG4maaaaa8aabaWdbiaaio % daaaaaaa!3B52! \sqrt[3]{{{{({5^2})}^3}}}\) \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 % qacqGH3daUaaa!384F! ÷ \) \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 % qadaGcaaWdaeaapeGaaiikaiaaikdapaWaaWbaaSqabeaapeGaaGOm % aaaakiaacMcapaWaaWbaaSqabeaapeGaaG4maaaaaeqaaaaa!3A73! \sqrt {{{({2^2})}^3}} \)
⇒ 2^(4) × 5^(2) ÷ 2^(3)
⇒ 16 × 25 ÷ 8 = 50
∴ \(\sqrt[3]{8^4}×\sqrt[3]{125^2}÷\sqrt{4^3}\) चे मूल्य 50 आहे.