قدر ناتج الجذور الآتية:

$\sqrt{45}$

$$\begin{gathered} \begin{array}{rl}& 36<45=\sqrt{45}>6\\ & 49>45=\sqrt{45}<7\\ & 6<\sqrt{45}<7\\ & 45-36=9,49-45=4\end{array} \\ \sqrt{45}\approx 6.9,6.8,6.7 \end{gathered}$$

تدرب وحل التمرينات

قدر ناتج الجذور الآتية:

$\sqrt[3]{13}$

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

$\sqrt{53}$

$$\begin{gathered} \begin{array}{rl}& 49<53=\sqrt{53}>7\\ & 64>53=\sqrt{53}<8\\ & 7<\sqrt{53}<8\\ & 53-49=4,64-53=11\end{array} \\ \sqrt{53}\approx 7.1,7.2,7.3 \end{gathered}$$

$\sqrt{123}$

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

$\sqrt{275}$

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

$\sqrt[3]{88}$

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

$\sqrt{45}$

$$\begin{gathered} \begin{array}{rl}& 36<45=\sqrt{45}>6\\ & 49>45=\sqrt{45}<7\\ & 6<\sqrt{45}<7\\ & 45-36=9,49-45=4\end{array} \\ \sqrt{45}\approx 6.9,6.8,6.7 \end{gathered}$$

$\sqrt{29}$

$$\begin{gathered} \begin{array}{rl}& 25<29=\sqrt{29}>5\\ & 36>29=\sqrt{29}<6\\ & 5<\sqrt{29}<6\\ & 36-29=7,29-25=4\end{array} \\ \sqrt{29}\approx 5.1,5.2,5.3 \end{gathered}$$

$\sqrt[3]{166}$

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

$\sqrt[3]{21}$

$$\begin{gathered} \begin{array}{rl}& 8<21\Rightarrow \sqrt[3]{21}>2\\ & 27>21\Rightarrow \sqrt[3]{21}<3\end{array} \\ \begin{array}{rl}& 2<\sqrt[3]{21}<3\\ & 27-21=6,21-8=7\end{array} \\ \sqrt[3]{21}\approx 2.9,2.8,2.7 \end{gathered}$$

$\sqrt[3]{910}$

$$\begin{gathered} \begin{array}{ll}729<910\Rightarrow & \sqrt[3]{910}>9\\ 1000>910\Rightarrow & \sqrt[3]{910}<10\end{array} \\ \begin{array}{rl}& 9<\sqrt[3]{910}<10\\ & 1000-910=90,910-729=181\end{array} \\ \sqrt[3]{910}\approx 9.9,9.8,9.7 \end{gathered}$$

$\sqrt{71}$

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

$\sqrt{175}$

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

$\sqrt[3]{710}$

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

$\sqrt[3]{202}$

$$\begin{gathered} \begin{array}{rl}& 125<202\Rightarrow \sqrt[3]{202}>5\\ & 216>202\Rightarrow \sqrt[3]{202}<6\end{array} \\ \begin{array}{rl}& 5<\sqrt[3]{202}<6\\ & 216-202=14,202-125=77\end{array} \\ \sqrt[3]{202}\approx 5.9,5.8,5.7 \end{gathered}$$

$\sqrt{412}$

$$\begin{gathered} \begin{array}{rl}& 400<412=\sqrt{412}>20\\ & 441>412=\sqrt{412}<21\\ & 20<\sqrt{412}<21\\ & 441-412=29,412-400=12\end{array} \\ \sqrt{412}\approx 20.1,20.2,20.3 \end{gathered}$$