Question 9 - Finding approximate value of numbers - Chapter 6 Class 12 Application of Derivatives

Last updated at August 7, 2026 by

Example 22 - Use differential to approximate (25)1/3 - Examples

Example 22 - Chapter 6 Class 12 Application of Derivatives - Part 2
Example 22 - Chapter 6 Class 12 Application of Derivatives - Part 3

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Question 9 Use differential to approximate 怖(25)怗^(1/3)Let š‘¦ =š‘„^(1/3) Where š‘„=27 and ā–³š‘„=āˆ’2 Since š’š =š’™^(šŸ/šŸ‘) š‘‘š‘¦/š‘‘š‘„=š‘‘(š‘„^(1/3) )/š‘‘š‘„ = 1/3 š‘„^(1/3 āˆ’ 1) = 1/3 š‘„^((āˆ’2)/3) š‘‘š‘¦/š‘‘š‘„=1/(3š‘„^(2/3) ) Now, āˆ†š’š=š’…š’š/š’…š’™ āˆ†š’™ āˆ†š‘¦= 1/(3š‘„^(2/3) ) āˆ†š‘„ Putting values āˆ†š‘¦= 1/(3(27)^(2/3) ) (āˆ’2) āˆ†š‘¦= (āˆ’2)/(3 Ɨ(3^3 )^(2/3) ) āˆ†š‘¦= (āˆ’2)/(3 Ɨ 3^2 ) āˆ†š‘¦= (āˆ’2)/27 āˆ†š’š=āˆ’šŸŽ.šŸŽšŸ•šŸ’ Now, (šŸšŸ“)^(šŸ/šŸ‘) =š’š+āˆ†š’š Putting values (25)^(1/3)=(27)^(1/3)āˆ’0.074 (25)^(1/3)=(3^3 )^(1/3)āˆ’0.074 (25)^(1/3)=3āˆ’0.074 (šŸšŸ“)^(šŸ/šŸ‘)=šŸ.šŸ—šŸšŸ” Hence, approximate value of (25)^(1/3) is šŸ.šŸ—šŸšŸ”

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