Question

Introdu factorii sub radical impunând condițiile necesare avolo unde este cazul :
a).
$3 \sqrt{5}$
b).
$7 \sqrt{6}$
c).
$- 9 \sqrt{2}$
d).
$- \frac{1}{2} \sqrt{3}$
e).
$\frac{3}{5} \sqrt{ \frac{1}{2} }$
f).
$\frac{5}{7} \sqrt{3}$
g).
$- \frac{2}{3} \sqrt{ \frac{3}{2} }$
h).
$0.(3) \sqrt{15}$
i).
$- 0.(1) \sqrt{2}$
Va rog repede dau coroana !!

Answer 1

$a)3 \sqrt{5} = \sqrt{ {3}^{2} \times 5} = \sqrt{9 \times 5} = \sqrt{45}$

$b)7 \sqrt{6} = \sqrt{ {7}^{2} \times 6} = \sqrt{49 \times 6} = \sqrt{294}$

$c) - 9 \sqrt{2} = \sqrt{( { - 9}^{2}) \times 2} = \sqrt{81 \times 2} = \sqrt{162}$

$d) - \frac{1}{2} \sqrt{3} = \sqrt{ { (- \frac{1}{2}) }^{2} \times 3} = \sqrt{ \frac{1}{4} \times 3} = \sqrt{ \frac{3}{4} }$

$e) \frac{3}{5} \sqrt{ \frac{1}{2} } = \sqrt{ ({ \frac{3}{5}) }^{2} \times \frac{1}{2} } = \sqrt{ \frac{9}{25} \times \frac{1}{2} } = \sqrt{ \frac{9}{50} }$

$f) \frac{5}{7} \sqrt{3} = \sqrt{ {( \frac{5}{7}) }^{2} \times 3 } = \sqrt{ \frac{25}{49} \times 3} = \sqrt{ \frac{75}{49} }$

$g) - \frac{2}{3} \sqrt{ \frac{3}{2} } = \sqrt{ {( - \frac{2}{3} )}^{2} \times \frac{3}{2} } = \sqrt{ \frac{4}{9} \times \frac{3}{2} } = \sqrt{ \frac{2}{3} }$

$h)0.(3) \sqrt{15} = \frac{3}{10} \sqrt{15} = \sqrt{ { (\frac{3}{10}) }^{2} \times 15} = \sqrt{ \frac{9}{100} \times 15 } = \sqrt{ \frac{135}{100} }$

$i) - 0.(1) \sqrt{2} = - \frac{1}{9} \sqrt{2} = \sqrt{ {( - \frac{1}{9} )}^{2} \times 2 } = \sqrt{ \frac{1}{81} \times 2 } = \sqrt{ \frac{2}{81} }$