求平方根的近似值─十分逼近法
使用十分逼近法求 $\sqrt 2$ 的近似值,過程如下:
(1) $\because 1^2=1$ , $(\sqrt2)^2=2$ , $2^2=4$
$\therefore 1\lt 2\lt 4$ $\Rightarrow \sqrt{1^2}\lt \sqrt{2}\lt \sqrt{2^2}$ $\Rightarrow 1\lt \sqrt{2}\lt 2$
(2) $\because 1.4^2=1.96$ , $(\sqrt2)^2=2$ , $1.5^2=2.25$
$\therefore 1.96\lt 2\lt 2.25$ $\Rightarrow \sqrt{1.4^2}\lt \sqrt{2}\lt \sqrt{1.5^2}$ $\Rightarrow 1.4\lt \sqrt{2}\lt 1.5$
(3) $\because 1.41^2=1.9881$ , $(\sqrt2)^2=2$ , $1.42^2=2.0164$
$\therefore 1.9881\lt 2\lt 2.0164$ $\Rightarrow \sqrt{1.41^2}\lt \sqrt{2}\lt \sqrt{1.42^2}$ $\Rightarrow 1.41\lt \sqrt{2}\lt 1.42$
(4) $\because 1.415^2=2.002225 \gt 2$
$\therefore \sqrt{1.415^2}\gt 2$ $\Rightarrow 1.415\gt \sqrt{2}$
故四捨五入得 $\sqrt2\Doteq 1.41$
觀念影片
8
|
(8)求平方根的近似值─十分逼近法8:50 |
|