# Simplify sqrt(18a^2)xx4sqrt(3a^2)?

Mar 29, 2017

$= 12 {a}^{2} \sqrt{6}$

#### Explanation:

$\sqrt{18 {a}^{2}} \cdot 4 \sqrt{3 {a}^{2}} = 4 \sqrt{18 {a}^{2} \cdot 3 {a}^{2}}$

$= 4 \sqrt{54 {a}^{4}} = 4 \sqrt{9 {a}^{4} \cdot 6}$

$= 4 \sqrt{9 {a}^{4}} \cdot \sqrt{6}$

$= 4 \cdot 3 {a}^{2} \cdot \sqrt{6}$

$= 12 {a}^{2} \sqrt{6}$

Mar 29, 2017

$12 {a}^{2} \sqrt{6}$

#### Explanation:

You are looking for squared values. These can be 'taken out' of the root.

Given:$\text{ } \sqrt{18 {a}^{2}} \times 4 \sqrt{3 {a}^{2}}$

We can 'extract' the ${a}^{2}$ giving:

$a \sqrt{18} \times 4 a \sqrt{3}$

3 is a prime number so that root can not be changed (at the moment).

Note that $18 \to 2 \times 9 \to 2 \times {3}^{2}$ giving:

$a \sqrt{2 \times {3}^{2}} \times 4 a \sqrt{3}$

We can 'extract' the ${3}^{2}$

$3 a \sqrt{2} \times 4 a \sqrt{3}$

Check the next step out on a calculator. It does work!

Combining the contents of the roots.

$3 a \times 4 a \times \sqrt{2 \times 3}$

$12 {a}^{2} \sqrt{6}$

Mar 29, 2017

color(red)(12a^2sqrt6

#### Explanation:

$\sqrt{18 {a}^{2}} \cdot 4 \sqrt{3 {a}^{2}}$

$\therefore = \sqrt{2 \cdot 3 \cdot 3 \cdot a \cdot a} \times 4 \sqrt{3 \cdot a \cdot a}$

color(red)(Note:

:.=color(red)(sqrta*sqrta=a or color(red)(sqrt(a*a)=a

$\therefore = 3 a \sqrt{2} \times 4 \cdot a \sqrt{3}$

$\therefore = 12 {a}^{2} \sqrt{2} \times \sqrt{3}$

$\therefore = 12 {a}^{2} \sqrt{2 \cdot 3}$

:.color(red)(=12a^2sqrt6