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根号で表された数の大小比較 ○根号の中の数が大きくなると,ルートの値も大きくなります.
【例】
(1) 2<3だから (小数で言えば1.41421...<1.73205...ですが,この小数が分からなくても大小比較ができるところがミソです)
(2) 5<6だから (小数で言えば2.23606...<2.44949...)
小数のルートも根号の中の数字の大小と一致します. (3) 1.2<1.3だから (1.095...<1.140...)
分数の大小でも同様です. (4) (0.5773...<0.7071...)
○負の根号の大小は,正の根号の大小と逆になります. ![]() (1) 2<3→ → (2) 5<7→ → ○根号の付いている数と根号の付いていない数の大小を比較するには,両方とも根号の付いた形に直せばよい
【例】
(1) 3と 3を (2) 4と |
【問題1】 次の各組の数の中で最も大きなものを選んでください. (クリックしてください) 解説 3<5<7だから 最も大きなものは 15<17<19だから 最も大きなものは ※これらの値が小数に直せなくても,大小の比較はできることに注意ましょう 解説 5<8<11だから 符号を変えると逆順になって 最も大きなものは 最も大きなものは4になります. 解説 0.32=0.09だから 最も大きなものは 解説 0.92=0.81だから 最も大きなものは0.9になります. |
【問題2】 次の各組の数の中で最も大きなものを選んでください. (クリックしてください) 解説 0.82=0.64だから また,分数を小数に直すと 最も大きなものは 分数を通分すると 最も大きなものは 分数を通分すると 符号を変えると 最も大きなものは |
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