Question

If o <y <x, which statement must be true?

Options

• \[\sqrt{x} - \sqrt{y} = \sqrt{x - y}\]

• \[\sqrt{x} + \sqrt{x} = \sqrt{2x}\]

• \[x\sqrt{y} = y\sqrt{x}\]

• \[\sqrt{xy} = \sqrt{x}\sqrt{y}\]

Answer 1

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.