# How do you simplify 5 sqrt48 - 4 sqrt 75 ?

Nov 3, 2015

$= 0$

#### Explanation:

$5 \sqrt{48} - 4 \sqrt{75}$

Here, we first prime factorise $48$ and $75$ to simplify the expression.

$\sqrt{48} = \sqrt{3 \cdot 2 \cdot 2 \cdot 2 \cdot 2} = \sqrt{3 \cdot {2}^{2} \cdot {2}^{2}}$
$= 4 \sqrt{3}$

Similarly:

$\sqrt{75} = \sqrt{3 \cdot 5 \cdot 5} = \sqrt{3 \cdot {5}^{2}}$
$= 5 \sqrt{3}$

5sqrt48 - 4sqrt75 = 5*color(blue)(4sqrt3) - 4*color(blue)(5sqrt3

$= 20 \sqrt{3} - 20 \sqrt{3}$

$= 0$