Question

Find the value of 3√{(35.285)²+(23.45)³}

\(\sqrt[3]{(35.285)^2+(23.45)^3}\)

Answer 1

Let x = \(\sqrt[3]{(35.285)^2+(23.45)^3}\)

Let a = (35.285)²

Taking log on both sides, we get

log₁₀ a = 2 log₁₀ (35.285) = 2 (1.5476)

\(\therefore\) log₁₀ a = 3.0952

\(\therefore\) a = antilog (3.0952) = 1.246 \(\times\) 10³ = 1246

Let b = (23.45)³

Taking log on both sides, we get

log₁₀ b = 3 log₁₀ (23.45) = 3(1.3701) = 4.1103

\(\therefore\) b = antilog (4.1103) = 1.289 \(\times\) 10⁴ = 12890

Taking log on both sides, we get

log₁₀x = \(\cfrac{1}{3}\)log₁₀ (14136) = \(\cfrac{1}{3}\)(4.1501)

\(\therefore\) log₁₀ x = 1.3834

\(\therefore\) x = antilog (1.3834) = 24.17