Bài 17 trang 14 SGK Toán 9 Tập 1

$a.\sqrt{0,09.64}=\sqrt{0,09}\cdot \sqrt{64}=\sqrt{0,3^2}\cdot \sqrt{8^2}=0,3.8=2,4$

$b.\sqrt{2^4\cdot (-7{)}^2}=\sqrt{2^4}\cdot \sqrt{(-0,7{)}^2}=\sqrt{{\left(2^2\right)}^2}.0,7=2^2\cdot 0,7=2,8$

$c.\sqrt{12,1.360}=\sqrt{121.36}=\sqrt{121}\cdot \sqrt{36}=\sqrt{{11}^2}\cdot \sqrt{6^2}=11.6=66$

$d.\sqrt{2^2\cdot 3^4}=\sqrt{2^2}\cdot \sqrt{3^4}=2\cdot \sqrt{{\left(3^2\right)}^2}={2.3}^2=18$

a) Ta có:

$\sqrt{0,09.64}=\sqrt{0,09}.\sqrt{64}$

$=\sqrt{(0,3{)}^2}.\sqrt{8^2}$

=|0,3|. |8|

=0,3.8

=2,4.

b) Ta có:

$\sqrt{2^4.(-7{)}^2}=\sqrt{2^4}.\sqrt{(-7{)}^2}$

$=\sqrt{(2^2{)}^2}.\sqrt{(-7{)}^2}$

$=\sqrt{4^2}.|-7|$

=|4|.|-7|

=4.7

=28.

c) Ta có:

$\sqrt{12,1.360}=\sqrt{12,1.(10.36)}$

$=\sqrt{(12,1.10).36}$

$=\sqrt{121.36}$

$=\sqrt{121}.\sqrt{36}$

$=\sqrt{{11}^2}.\sqrt{6^2}$

=|11|.|6|

=11.6

=66.

d) Ta có:

$\sqrt{2^2{.3}^4}=\sqrt{2^2}.\sqrt{3^4}$

$=\sqrt{2^2}.\sqrt{(3^2{)}^2}$

$=\sqrt{2^2}.\sqrt{9^2}$

=|2|.|9|

=2.9

=18.