Question

Please show work!!!!!!!!!

Answer 1

83 + 12
`√(35)`

Explanation:

Using the rules of radicals

•
`√(a)` ×
`√(b)` ⇔
`√(ab)`

•
`√(a)` ×
`√(a)` = a

Given

(2
`√(5)` + 3
`√(7)`)²

= (2
`√(5)` + 3
`√(7)`)(2
`√(5)` + 3
`√(7)`)

Expand factors using FOIL

= (2
`√(5)`)² + 6
`√(35)` + 6
`√(35)` + (3
`√(7)`)²

=20 + 12
`√(35)` + 63

= 83 + 12
`√(35)`

Answer 2

83

Explanation:

(2((sqrt)(5))+3((sqrt)(7)))^2

is the same as every individual term inside to the power of 2

(2^2 x (root 5 )^2 + 3^2 x (root 7)^2)

any root squared will become the number inside the root by itself, i.e sqrt of 8^2 will become 8

((4x5) + (9x7))

= 20+63

=83