Advertisements
Advertisements
Question
If o <y <x, which statement must be true?
Options
\[\sqrt{x} - \sqrt{y} = \sqrt{x - y}\]
\[\sqrt{x} + \sqrt{x} = \sqrt{2x}\]
\[x\sqrt{y} = y\sqrt{x}\]
\[\sqrt{xy} = \sqrt{x}\sqrt{y}\]
Advertisements
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.
APPEARS IN
RELATED QUESTIONS
If 49392 = a4b2c3, find the values of a, b and c, where a, b and c are different positive primes.
Assuming that x, y, z are positive real numbers, simplify the following:
`(x^-4/y^-10)^(5/4)`
Show that:
`1/(1+x^(a-b))+1/(1+x^(b-a))=1`
Show that:
`(a^(x+1)/a^(y+1))^(x+y)(a^(y+2)/a^(z+2))^(y+z)(a^(z+3)/a^(x+3))^(z+x)=1`
Write \[\left( 625 \right)^{- 1/4}\] in decimal form.
If 24 × 42 =16x, then find the value of x.
Write the value of \[\sqrt[3]{125 \times 27}\].
The value of x − yx-y when x = 2 and y = −2 is
Which one of the following is not equal to \[\left( \sqrt[3]{8} \right)^{- 1/2} ?\]
If a, m, n are positive ingegers, then \[\left\{ \sqrt[m]{\sqrt[n]{a}} \right\}^{mn}\] is equal to
