Rút gọn biểu thức: A= căn 40^2 - 24^2

Giải Toán 9 Bài tập cuối chương 3 trang 72

Bài 3 trang 72 Toán 9 Tập 1: Rút gọn biểu thức:

a. $A=\sqrt{{40}_2^{}-{24}_2^{}}$;

b. $B=\left(\sqrt{12}+2\sqrt{3}-\sqrt{27}\right).\sqrt{3}$;

c. $C=\frac{\sqrt{{63}_3^{}+1}}{\sqrt{{63}_2^{}-62}}$;

d. $D=\sqrt{60}-5\sqrt{\frac{3}{5}}-3\sqrt{\frac{5}{3}}$.

Lời giải:

a. $A=\sqrt{{40}_2^{}-{24}_2^{}}$

$\begin{array}{l}=\sqrt{\left(40-24\right)\left(40+24\right)}\\ =\sqrt{16.64}=\sqrt{16}.\sqrt{64}\\ =4.8=32\end{array}$

b. $B=\left(\sqrt{12}+2\sqrt{3}-\sqrt{27}\right).\sqrt{3}$

$\begin{array}{l}=\left(\sqrt{12}+\sqrt{12}-\sqrt{27}\right).\sqrt{3}\\ =\left(2\sqrt{12}-\sqrt{27}\right).\sqrt{3}\\ =2\sqrt{36}-\sqrt{81}\\ =12-9\\ =3\end{array}$

c. $C=\frac{\sqrt{{63}^3+1}}{\sqrt{{63}^2-62}}$

$\begin{array}{l}=\frac{\sqrt{\left(63+1\right)\left({63}_2^{}-63+1\right)}}{\sqrt{{63}_2^{}-62}}\\ =\frac{\sqrt{64.\left({63}_2^{}-62\right)}}{\sqrt{{63}_2^{}-62}}\\ =\frac{\sqrt{64}.\sqrt{{63}_2^{}-62}}{\sqrt{{63}_2^{}-62}}\\ =\sqrt{64}\\ =8\end{array}$

d. $D=\sqrt{60}-5\sqrt{\frac{3}{5}}-3\sqrt{\frac{5}{3}}$

$\begin{array}{l}=\sqrt{4.15}-5\frac{\sqrt{3}}{\sqrt{5}}-3\frac{\sqrt{5}}{\sqrt{3}}\\ =\frac{2\sqrt{15}.\sqrt{15}}{\sqrt{15}}-\frac{5\sqrt{3}.\sqrt{3}}{\sqrt{15}}-\frac{3\sqrt{5}.\sqrt{5}}{\sqrt{15}}\\ =\frac{30}{\sqrt{15}}-\frac{15}{\sqrt{15}}-\frac{15}{\sqrt{15}}\\ =\frac{0}{\sqrt{15}}=0\end{array}$