# How do you simplify 3sqrt50-3sqrt32?

Feb 9, 2017

$3 \sqrt{2}$

#### Explanation:

$3 \sqrt{50} - 3 \sqrt{32}$:

the surds in the question are not simplified. therefore they can be broken down further.

$3 \sqrt{50}$:

factors of $50$: $1 , 2 , 5 , 10 , 25 , 50.$

$\sqrt{25} = 5$

$\therefore 3 \sqrt{50} = 3 \cdot \sqrt{25} \cdot \sqrt{2}$
$= 3 \cdot 5 \cdot \sqrt{2}$
$= 15 \sqrt{2}$

$3 \sqrt{32}$:

factors of $32$: $1 , 2 , 4 , 8 , 16 , 32$

$\sqrt{16} = 4$

$\therefore 3 \sqrt{32} = 3 \cdot \sqrt{16} \cdot \sqrt{2}$
$= 3 \cdot 4 \cdot \sqrt{2}$
$= 12 \sqrt{2}$

the question is simplified to $15 \sqrt{2} - 12 \sqrt{2}$

law of surds:
$a \sqrt{b} + c \sqrt{b} = \left(a + c\right) \sqrt{b}$

$15 \sqrt{2} + - 12 \sqrt{2} = \left(15 - 12\right) \sqrt{2}$
$= 3 \sqrt{2}$

Feb 9, 2017

$3 \sqrt{2}$

#### Explanation:

$3 \sqrt{50} - 3 \sqrt{32}$

:.=3*sqrt(2*5*5)-3*sqrt(2*2*2*2*2

$\therefore = 3 \cdot \sqrt{2} \cdot \sqrt{5} \cdot \sqrt{5} - 3 \cdot \sqrt{2} \cdot \sqrt{2} \cdot \sqrt{2} \cdot \sqrt{2} \cdot \sqrt{2}$

note: $\sqrt{5} \cdot \sqrt{5} = 5$ and$\sqrt{2} \cdot \sqrt{2} = 2$

$\therefore = 3 \cdot \sqrt{2} \cdot 5 - 3 \cdot 2 \cdot 2 \cdot \sqrt{2}$

$\therefore = 15 \cdot \sqrt{2} - 12 \cdot \sqrt{2}$

$\therefore = 3 \sqrt{2} \left(5 - 4\right)$

$\therefore = 3 \sqrt{2} \cdot 1$

$\therefore = 3 \sqrt{2}$