SOLUTION: simplify: sqrt 81c^5d^4
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Question 6305
:
simplify:
sqrt 81c^5d^4
Answer by
AnlytcPhil(1810)
(
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simplify:
`______
Ö
81c
5
d
4
`
Prime factor 81 = 9·9 = 3·3·3·3
Prime factor c
5
= c·c·c·c·c
Prime factor d
4
= d·d·d·d
`______
Ö
81c
5
d
4
=
`_________________________
Ö
3·3·3·3·c·c·c·c·c·d·d·d·d =
`_____________________________________
Ö
(3·3)·(3·3)·(c·c)·(c·c)·c·(d·d)·(d·d) =
`_______________________________
Ö
(3
2
)·(3
2
)·(c
2
)·(c
2
)·c·(d
2
)·(d
2
) =
`__ `__` __`__ `_` __` __
Ö
3
2
·
Ö
3
2
·
Ö
c
2
·
Ö
c
2
·
Ö
c·
Ö
d
2
·
Ö
d
2
=
` ` ` ` ` ` ` ` `_
`3 · 3 · c · c ·
Ö
c· d · d =
` ` ``_
9·c
2
·
Ö
c·d
2
` ` ` _
9c
2
d
2
Ö
c
`
Edwin
