Обчисліть:
1) $\sqrt{25};$
2) $\sqrt{0{,}09};$
3) $\sqrt{1\frac{11}{25}};$
4) $\sqrt{64}-2\sqrt{0{,}04};$
5) $-5\sqrt{0{,}16};$
6) $4\sqrt{20\frac{1}{4}};$
7) $\sqrt{{13}^2-{12}^2};$
8) $\sqrt{2\left(0{,}3^2+0{,}41\right)}.$
Розв'язок:
1) $\sqrt{25}=5;$
2) $\sqrt{0{,}09}=0{,}3;$
3) $\sqrt{1\frac{11}{25}}=\sqrt{\frac{36}{25}}=\frac{6}{5}=1{,}2;$
4) $\sqrt{64}-2\sqrt{0{,}04}=8-2\cdot0{,}2=$
$= 8-0{,}4=7{,}6;$
5) $-5\sqrt{0{,}16}=-5\cdot0{,}4=-2;$
6) $4\sqrt{20\frac{1}{4}}=4\sqrt{\frac{81}{4}}=4\cdot\frac{9}{2}=18;$
7) $\sqrt{{13}^2-{12}^2}=\sqrt{169-144}=$
$= \sqrt{25}=5;$
8) $\sqrt{2(0{,}3^2+0{,}41)}=$
$= \sqrt{2(0{,}09+0,41)}=\sqrt{2\cdot0{,}5}=$
$= \sqrt1=1.$