Question

Class 11-Physics


Evaluate (126)^2/3.​

Answer 1

${126}^{ \frac{2}{3} } \\ \\ (126 \times 126)^{ \frac{1}{3} } \\ \\ (7 \times 2 \times {3}^{2} \times 7 \times 2 \times {3}^{2} )^{ \frac{1}{3} } \\ \\ ( {3}^{4} {2}^{2} 7^{2} )^{ \frac{1}{3} } \\ \\ 3({2}^{2} {7}^{2} 3) ^{ \frac{1}{3} } \\ \\ let \: \: ({2}^{2} {7}^{2} 3) ^{ \frac{1}{3} } = x \\ \\ taking \: log_{10} \: \: on \: both \: sides \\ \\ \frac{2}{3} log_{10}2 + \frac{2}{3} log_{10}7 + \frac{1}{3} log_{10}(3) = log_{10}x \\ \\ \frac{2}{3} (0.3010) + \frac{2}{3} (0.8450) + \frac{1}{3} (0.4771) = log_{10}x \\ \\ \frac{2.7691}{3} = log_{10}x \\ \\ x = {10}^{ \frac{2.7691}{3} } \\ \\ x = 8.376 \\ \\ now \\ \\ {126}^{ \frac{2}{3} } . = . > \: 3x \\ \\ {126}^{ \frac{2}{3} } . = . > \: 25.128 \\ \\ \\ . > \: refers \: to \: approximation \\ \\ \\ for \: log \: and \: antilog \: values \: refer \:log \: table$

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