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[tex]\sqrt{2\frac{2}{49}}=\sqrt{\frac{2\cdot49+2}{49}}=\sqrt{\frac{98+2}{49}}=\sqrt{\frac{100}{49}}=\sqrt{\frac{10^2}{7^2}}=\frac{10}{7}=1\frac{3}{7}\\\\\\\sqrt{6\frac{1}{4}}=\sqrt{\frac{6\cdot4+1}{4}}=\sqrt{\frac{24+1}{4}}=\sqrt{\frac{25}{4}}=\sqrt{\frac{5^2}{2^2}}=\frac{5}{2}=2\frac{1}{2}\\\\\\\sqrt{2\frac{7}{9}}=\sqrt{\frac{2\cdot9+7}{9}}=\sqrt{\frac{18+7}{9}}=\sqrt{\frac{25}{9}}=\sqrt{\frac{5^2}{3^2}}=\frac{5}{3}=1\frac{2}{3}[/tex]
