تدرب وحل التمرينات

قدر ناتج الجذور الآتية:

$\sqrt[3]{13}$

$$\begin{gathered} \begin{array}{rl}& 8<13=\sqrt[3]{13}>2\\ & 27>13\Rightarrow \sqrt[3]{13}<3\\ & 2<\sqrt[3]{13}<3\\ & 13-8=5,27-13=14\end{array} \\ \sqrt[3]{13}\approx 2.1,2.2,2.3 \end{gathered}$$

$\sqrt[3]{88}$

$$\begin{gathered} \begin{array}{rl}& 64<88=\sqrt[3]{88}>4\\ & 125>88=\sqrt[3]{88}<5\end{array} \\ \begin{array}{rl}& 4<\sqrt[3]{88}<5\\ & 88-64=24,125-88=37\end{array} \\ \sqrt[3]{88}\approx 4.1,4.2,4.3 \end{gathered}$$

$\sqrt{123}$

$$\begin{gathered} \begin{array}{rl}& 121<123=\sqrt{123}>11\\ & 144>123=\sqrt{123}<12\\ & 11<\sqrt{123}<12\\ & 123-121=2,144-123=21\end{array} \\ \sqrt{123}\approx 11.1,11.2,11.3 \end{gathered}$$

$\sqrt{275}$

$$\begin{gathered} \begin{array}{rl}& 256<275=\sqrt{275}>16\\ & 289>275=\sqrt{275}<17\\ & 16<\sqrt{275}<17\\ & 275-256=19.289-275=14\end{array} \\ \sqrt{275}\approx 16.9,16.8,16.7 \end{gathered}$$

$\sqrt[3]{166}$

$$\begin{gathered} \begin{array}{rl}& 125<166\Rightarrow \sqrt[3]{166}>5\\ & 216>166\Rightarrow \sqrt[3]{166}<6\end{array} \\ \begin{array}{rl}& 5<\sqrt[3]{166}<6\\ & 216-166=50,166-125=41\end{array} \\ \sqrt[3]{166}\approx 5.1,5.2,5.3 \end{gathered}$$

$\sqrt{175}$

$$\begin{gathered} \begin{array}{rl}& 169<175=\sqrt{175}>13\\ & 196>175=\sqrt{175}<14\\ & 13<\sqrt{175}<14\\ & 196-175=21,175-169=0\end{array} \\ \sqrt{175}\approx 13.1,13.2,13.3 \end{gathered}$$

$\sqrt[3]{710}$

$$\begin{gathered} \begin{array}{rl}& 512<710\Rightarrow \sqrt[3]{710}>8\\ & 729>710\Rightarrow \sqrt[3]{710}<9\end{array} \\ \begin{array}{rl}& 8<\sqrt[3]{710}<9\\ & 729-710=19,710-512=198\end{array} \\ \sqrt[3]{710}\approx 8.9,8.8,8.7 \end{gathered}$$

$\sqrt{71}$

$$\begin{gathered} \begin{array}{rl}& 64<71=\sqrt{71}>8\\ & 81>71=\sqrt{71}<9\\ & 8<\sqrt{71}<9\\ & 81-71=10,71-64=7\end{array} \\ \sqrt{71}\approx 8.1,8.2,8.3 \end{gathered}$$