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Question
If o <y <x, which statement must be true?
Options
\[\sqrt{x} - \sqrt{y} = \sqrt{x - y}\]
\[\sqrt{x} + \sqrt{x} = \sqrt{2x}\]
\[x\sqrt{y} = y\sqrt{x}\]
\[\sqrt{xy} = \sqrt{x}\sqrt{y}\]
Solution
We have to find which statement must be true?
Given `0<y<x,`
Option (a) :
Left hand side:
`sqrtx-sqrty= sqrtx -sqrty`
Right Hand side:
`sqrt(x-y)= sqrt(x-y)`
Left hand side is not equal to right hand side
The statement is wrong.
Option (b) :
`sqrtx +sqrtx = sqrt(2x)`
Left hand side:
`sqrtx +sqrtx = 2sqrtx`
Right Hand side:
`sqrt(2x) = sqrt(2x)`
Left hand side is not equal to right hand side
The statement is wrong.
Option (c) :
`xsqrty = ysqrtx`
Left hand side:
`xsqrty = ysqrtx`
Right Hand side:
`ysqrtx = y sqrtx`
Left hand side is not equal to right hand side
The statement is wrong.
Option (d) :
`sqrt(xy) = sqrtxsqrty`
Left hand side:
`sqrt(xy) = sqrt(xy)`
Right Hand side:
`sqrtxsqrty = sqrtx xx sqrty`
`= sqrt(xy)`
Left hand side is equal to right hand side
The statement is true.
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