Question

If $x=\sqrt{12}-\sqrt{9},y=\sqrt{13}-\sqrt{10}$ and $z=\sqrt{11}-\sqrt{8}$, then which of the following is true?

• A. $z>x>y$
• B. $z>y>x$
• C. $y>x>z$
• D. $y>z>x$

Answer 1

The correct option is A $z>x>y$

$x=\sqrt{12}-\sqrt{9}$

$x=2\sqrt{3}-3$

$x=2\left(1.73\right)-3$

$x=3.46-3$

$\therefore$ $x=0.46$ ----- ( 1 )

Now,

$y=\sqrt{13}-\sqrt{10}$

$y=3.60-3.16$

$\therefore$ $y=0.44$ ---- ( 2 )

Now,

$z=\sqrt{11}-\sqrt{8}$

$z=3.32-2.83$

$\therefore$ $z=0.49$ ---- ( 3 )

From ( 1 ), ( 2 ) and ( 3 )

$\Rightarrow$ $0.49>0.46>0.44$

$\therefore$ $z>x>y$