Question

Sqaure root of 5 (u-1)(u^5+u^4+u^3+u^2+u+1)

Answer 1

GIVEN:


`5(u - 1)( {u}^(5) + {u}^(4) + {u}^(3) + {u}^(2) + u + 1)`

remember:


`√(u) = {u}^{ (1)/(2) }`

And


`{u}^(n) * {u}^(m) = {u}^(n + m)`

SOLVE:

start by multiplying the factors:


`5( ({u}^(6) + {u}^(5) + {u}^(4) + {u}^(3) + {u}^(2) + u ) - ( {u}^(5) + {u}^(4) + {u}^(3) + {u}^(2) + u + 1))`

simplify by combing like terms. Most terms subtract off, leaving:


`5( {u}^(6) - 1)`

This can be factored, but it is not a perfect square, which is really what we need to take the square root.


`5( {u}^(3) - 1)( {u}^(3) + 1)`

I'm not exactly sure what form they want the answer in...

so taking the square root:


`\sqrt{5( {u}^(6) - 1) } = {(5( {u}^(6) - 1))}^{ (1)/(2) }`

so my best answer is:


`{5}^{ (1)/(2) } * {( {u}^(6) - 1)}^{ (1)/(2) }`
or the more factored form:


`{5}^{ (1)/(2) } { ({u}^(3) - 1)}^{ (1)/(2) } { ({u}^(3) + 1 )}^{ (1)/(2) }`

I'm not sure how else to solve it. Taking the square root doesn't work out super well, so I left it in the most simple form I could.

sorry for not coming to a definitive answer!