Question

Help with radicals, questions down in attachments.

Answer 1

we can't solve first 2 because of missing diagramd
but, longest side=hypotonuse=c
other 2 sides=legs=a and b
a^2+b^2=c^2
$\sqrt{a^{2}+b^{2}}=c$

last 2
1.
remember that
longest side<sum of other 2 sides or else you can't make a traignel
5+7=12
12<13
13 is longest side
13<12 is false
therefor it is false that it is a triangle
not a triangle


2.
$\sqrt{ \frac{x}{y} } = \frac{ \sqrt{x} }{ \sqrt{y} }$ so
$\sqrt{ \frac{20}{7} } = \frac{ \sqrt{20} }{ \sqrt{7} }$ =$\frac{4\sqrt{5} }{\sqrt{7} }$
rationalize denomeator by multplying by $\frac{ \sqrt{7} }{ \sqrt{7} }$

$\frac{4\sqrt{35} }{7}$