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:


`( √(15) )/( √(15) ) = 1`

so , now multiply:


`(3)/( √(15) ) * ( √(15) )/( √(15) ) = (3 √(15) )/(15) = ( √(15) )/(5)`

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