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Last updated at April 19, 2021 by Teachoo

Example 22 Use differential to approximate γ(25)γ^(1/3)Let π¦ =π₯^(1/3) Where π₯=27 and β³π₯=β2 Since π =π^(π/π) ππ¦/ππ₯=π(π₯^(1/3) )/ππ₯ = 1/3 π₯^(1/3 β 1) = 1/3 π₯^((β2)/3) ππ¦/ππ₯=1/(3π₯^(2/3) ) Now, βπ=π π/π π βπ βπ¦= 1/(3π₯^(2/3) ) βπ₯ Putting values βπ¦= 1/(3(27)^(2/3) ) (β2) βπ¦= (β2)/(3 Γ(3^3 )^(2/3) ) βπ¦= (β2)/(3 Γ 3^2 ) βπ¦= (β2)/27 βπ=βπ.πππ Now, (ππ)^(π/π) =π+βπ Putting values (25)^(1/3)=(27)^(1/3)β0.074 (25)^(1/3)=(3^3 )^(1/3)β0.074 (25)^(1/3)=3β0.074 (ππ)^(π/π)=π.πππ Hence, approximate value of (25)^(1/3) is π.πππ