Question

PLEASE help with these questions?? there are 7 of them! Thank you!!

Answer 1

We know in these kind of triangles that have a 90 degrees angle, we can do:

${a}^{2} + {b}^{2} = {c}^{2}$

so the first question:

$\sqrt{ {99}^{2} + {20}^{2} } = 101$

and then:

$b = \sqrt{ {17}^{2} - {15}^{2} } = 8$

so , when you want to rationalize , usually you must multiply the irrational factor as 1:

$\frac{ \sqrt{15} }{ \sqrt{15} } = 1$

so , now multiply:

$\frac{3}{ \sqrt{15} } \times \frac{ \sqrt{15} }{ \sqrt{15} } = \frac{3 \sqrt{15} }{15} = \frac{ \sqrt{15} }{5}$

in the next question,we know negative numbers in radical don't have any solution so 2 is correct,