Question

`4 √(40) + 7 √(160)`
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Answer 1

36
`√(10)`

Explanation:

Using the rule of radicals

`√(a)` ×
`√(b)` ⇔
`√(ab)`

Simplifying the radicals in the expression

`√(40)`

=
`√(4(10))`

=
`√(4)` ×
`√(10)` = 2
`√(10)`

`√(160)`

=
`√(16(10))`

=
`√(16)` ×
`√(10)` = 4
`√(10)`

Thus

4
`√(40)` + 7
`√(160)`

= 4 × 2
`√(10)` + 7 × 4
`√(10)`

= 8
`√(10)` + 28
`√(10)`

= 36
`√(10)`

Answer 2

Explanation:

4
`4√(40) + 7 √(160) = 4√(2*2*2*5)  + 7√(4*4*5*2)\\  = 4*2√(10)  + 7*4√(10)\\ = 8√(10) + 28√(10) \\`

= (8 + 28)√10

= 36√10