we know in these kind of triangles that have a 90 degrees angle, we can do:
[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]
so the first question:
[tex] \sqrt{ {99}^{2} + {20}^{2} } = 101[/tex]
and then:
[tex]b = \sqrt{ {17}^{2} - {15}^{2} } = 8[/tex]
so , when you want to rationalize , usually you must multiply the irrational factor as 1:
[tex] \frac{ \sqrt{15} }{ \sqrt{15} } = 1[/tex]
so , now multiply:
[tex] \frac{3}{ \sqrt{15} } \times \frac{ \sqrt{15} }{ \sqrt{15} } = \frac{3 \sqrt{15} }{15} = \frac{ \sqrt{15} }{5} [/tex]
in the next question,we know negative numbers in radical don't have any solution so 2 is correct,
