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Ҳисоб кунед:

\(\sqrt[3]{\underbrace{370370...037}_{89}-\underbrace{11...1}_{30}\underbrace{00...0}_{30}}\)

\(\sqrt[3]{\underbrace{370370...037}_{89}-\underbrace{11...1}_{30}\underbrace{00...0}_{30}}=\)

\(=\sqrt{37\cdot(10^{87}+10^{84}+...+10^0)-\underbrace{11...1}_{30}\cdot10^{30}}=\)

\(=\sqrt[3]{37\cdot\frac{10^{90}-1}{10^3-1}-\frac{1}{9}\cdot(10^{30}-1)\cdot10^{30}}=\)

\(=\sqrt[3]{37\cdot\frac{10^{90}-1}{999}-\frac{1}{9}\cdot(10^{30}-1)\cdot10^{30}}=\)

\(=\sqrt[3]{\frac{10^{90}-1}{27}-\frac{(10^{30}-1)\cdot10^{30}}{9}}=\)

\(=\sqrt[3]{\frac{10^{90}-1}{27}-\frac{10^{60}-10^{30}}{9}}=\)

\(=\sqrt[3]{\frac{10^{90}-3\cdot10^{60}+3\cdot10^{30}-1}{27}}=\)

\(=\sqrt[3]{\frac{(10^{30}-1)^3}{3^3}}=\)

\(=\frac{10^{30}-1}{3}=\)

\(=\underbrace{33...3}_{30}\)

Ҷавоб: \(\underbrace{33...3}_{30}\)