Ҳисоб кунед:

\(\sqrt{4444488889}\)

\(\sqrt{4444488889}=\sqrt{4444444444+44444+1}=\)

\(=\sqrt{4\cdot1111111111+4\cdot11111+1}=\sqrt{\frac{1}{9}\cdot(4\cdot9999999999+4\cdot99999+9)}=\)

\(=\frac{1}{3}\cdot\sqrt{4\cdot9999999999+4\cdot99999+9}=\frac{1}{3}\cdot\sqrt{4\cdot(10^{10}-1)+4\cdot(10^5-1)+9}=\)

\(=\frac{1}{3}\cdot\sqrt{4\cdot10^{10}-4+4\cdot10^5-4+9}=\frac{1}{3}\cdot\sqrt{4\cdot10^{10}+4\cdot10^5+1}=\)

\(=\frac{1}{3}\cdot\sqrt{(2\cdot10^5)^2+2\cdot(2\cdot10^5)\cdot1+1^2}=\)

\(=\frac{1}{3}\cdot\sqrt{(2\cdot10^5+1)^2}=\frac{1}{3}\cdot(2\cdot10^5+1)=\)

\(=\frac{1}{3}\cdot200001=66667\)

\(\sqrt{4444488889}=66667\)

Ҷавоб: 66667