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(5−3)3(\sqrt{5}-3)^3

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Full solution

Q. (5−3)3(\sqrt{5}-3)^3
  1. Expand Expression: Expand the expression using the binomial theorem or by multiplying (5−3)(\sqrt{5}-3) by itself three times.\newline(5−3)3=(5−3)×(5−3)×(5−3)(\sqrt{5}-3)^3 = (\sqrt{5}-3) \times (\sqrt{5}-3) \times (\sqrt{5}-3)
  2. Multiply First Two Factors: Multiply the first two factors (5−3)(\sqrt{5}-3) and (5−3)(\sqrt{5}-3).(5−3)×(5−3)=(5)2−2×3×5+32=5−6×5+9=14−6×5(\sqrt{5}-3) \times (\sqrt{5}-3) = (\sqrt{5})^2 - 2\times3\times\sqrt{5} + 3^2 = 5 - 6\times\sqrt{5} + 9 = 14 - 6\times\sqrt{5}
  3. Multiply Result with Remaining Factor: Multiply the result from Step 22 by the remaining factor (5−3)(\sqrt{5}-3).(14−65)×(5−3)(14 - 6\sqrt{5}) \times (\sqrt{5}-3)=145−42−655+185= 14\sqrt{5} - 42 - 6\sqrt{5}\sqrt{5} + 18\sqrt{5}=145−42−6×5+185= 14\sqrt{5} - 42 - 6\times 5 + 18\sqrt{5}=145+185−42−30= 14\sqrt{5} + 18\sqrt{5} - 42 - 30=(14+18)5−72= (14 + 18)\sqrt{5} - 72=325−72= 32\sqrt{5} - 72

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