Question

How do you rationalize the denominator and simplify `4sqrt(7/(2z^2))`?

Answer 1

`color(blue)(4sqrt(7/(2z^2))=(2sqrt(14))/z)`

`color(red)(root4(7/(2z^2))=root4(56z^2)/(2z))`

Explanation:

If the given is to simplify `4sqrt(7/(2z^2)`

The solution:

`4sqrt(7/(2z^2))=4sqrt(7/(2z^2)*2/2)=4sqrt(14/(4z^2))=(4sqrt(14))/(2z)=(2sqrt(14))/z`

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If the given is to simplify `root4(7/(2z^2))`

The solution:

`root4(7/(2z^2))=root4(7/(2z^2)*((8z^2)/(8z^2)))=root4((56z^2)/(16z^4))=root4(56z^2)/(2z)`

God bless....I hope the explanation is useful.