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Roots of rational numbers

nd the cube root of each number.\newlineI. 1643= \sqrt[3]{\frac{1}{64}}= 8273= \sqrt[3]{\frac{8}{27}}= 5123= \sqrt[3]{512}= \newline22. 03= \sqrt[3]{0}= 641253= \sqrt[3]{\frac{64}{125}}= 13= \sqrt[3]{1}= \newline33. 82163= \sqrt[3]{\frac{8}{216}}= 1253433= \sqrt[3]{\frac{125}{343}}= 643= \sqrt[3]{64}= \newlinetimate the following cube roots.\newline44. 103 \sqrt[3]{10} is between and but closer to\newline55. 8273= \sqrt[3]{\frac{8}{27}}= 00 is between and but closer to\newline66. 8273= \sqrt[3]{\frac{8}{27}}= 11 is between and but closer to\newline77. 8273= \sqrt[3]{\frac{8}{27}}= 22 is between and but closer to\newline88. 8273= \sqrt[3]{\frac{8}{27}}= 33 is between and but closer to\newlineChapter 22,\newlinesectrum Math\newlineRational and Irrational Number Rel\newlinerade 88
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Example 55: Express −2149 \frac{-21}{49} as a rational numbor with denominator 77 .\newlineSolution: To get denominator 77 , we must divide 4949 by 77 .\newlineTherefore, −21+749+7=−37 \quad \frac{-21+7}{49+7}=\frac{-3}{7} .\newlineHence, −37 \frac{-3}{7} is the required rational number.\newlineWorksheet 22\newline11. In each of the following cases, show that the rational numbers are equivalent,\newline(i) 49 \frac{4}{9} and 4499 \frac{44}{99} \newline(ii) 7−3 \frac{7}{-3} and 35−15 \frac{35}{-15} \newline(iii) −35 \frac{-3}{5} and −1220 \frac{-12}{20} \newline22. In each of the following cases, show that rational numbers are not equivalent.\newline(i) 49 \frac{4}{9} and −21+749+7=−37 \quad \frac{-21+7}{49+7}=\frac{-3}{7} 00\newline(ii) −21+749+7=−37 \quad \frac{-21+7}{49+7}=\frac{-3}{7} 11 and −21+749+7=−37 \quad \frac{-21+7}{49+7}=\frac{-3}{7} 22\newline(iii) −21+749+7=−37 \quad \frac{-21+7}{49+7}=\frac{-3}{7} 33 and −21+749+7=−37 \quad \frac{-21+7}{49+7}=\frac{-3}{7} 44\newline33. Write three rational numbers, equivalent to each of the following:\newline(i) −21+749+7=−37 \quad \frac{-21+7}{49+7}=\frac{-3}{7} 55\newline(ii) −21+749+7=−37 \quad \frac{-21+7}{49+7}=\frac{-3}{7} 66\newline(iii) −21+749+7=−37 \quad \frac{-21+7}{49+7}=\frac{-3}{7} 77\newline(iv) −21+749+7=−37 \quad \frac{-21+7}{49+7}=\frac{-3}{7} 88\newline44. Express −21+749+7=−37 \quad \frac{-21+7}{49+7}=\frac{-3}{7} 99 as rational number with numerator,\newline(i) −21-21\newline(ii) 150150\newlineExpress −37 \frac{-3}{7} 00 as a rational number with denominator,\newline(i) 8484\newline(ii) −28-28\newlineExpress −37 \frac{-3}{7} 11 as a rational number with numerator 55 .\newlinexpress −37 \frac{-3}{7} 22 as a rational number with denominator 88.\newlineid equivalent forms of the rational numbers having a common denominator in he following collections of rational numbers.\newline25,613 \frac{2}{5}, \frac{6}{13} \newline(ii) −37 \frac{-3}{7} 33\newline(iii) −37 \frac{-3}{7} 44\newline66
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