Simplify $\sqrt{18 a^{2}} \times 4 \sqrt{3 a^{2}}$ $sqrt(18a^2)xx4sqrt(3a^2)$ ?

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Simplify $\sqrt{18 a^{2}} \times 4 \sqrt{3 a^{2}}$ $sqrt(18a^2)xx4sqrt(3a^2)$ ?

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Answer 1 · 2017-03-29T09:08:18

$= 12 a^{2} \sqrt{6}$ $= 12 a^2 sqrt6$

Explanation:

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

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

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

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

$= 12 a^{2} \sqrt{6}$ $= 12 a^2 sqrt6$

Answer 2 · 2017-03-29T09:57:06

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

Explanation:

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

Given: $\sqrt{18 a^{2}} \times 4 \sqrt{3 a^{2}}$ $" "sqrt(18a^2)xx4sqrt(3a^2)$

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

$a \sqrt{18} \times 4 a \sqrt{3}$ $asqrt(18)xx4asqrt(3)$

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

Note that $18 \to 2 \times 9 \to 2 \times 3^{2}$ $18->2xx9->2xx3^2$ giving:

$a \sqrt{2 \times 3^{2}} \times 4 a \sqrt{3}$ $asqrt(2xx3^2)xx4asqrt(3)$

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

$3 a \sqrt{2} \times 4 a \sqrt{3}$ $3asqrt(2)xx4asqrt(3)$

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

Combining the contents of the roots.

$3 a \times 4 a \times \sqrt{2 \times 3}$ $3axx4axxsqrt(2xx3)$

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

Answer 3 · 2017-03-29T09:58:27

$12 a^{2} \sqrt{6}$ $color(red)(12a^2sqrt6$

Explanation:

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

$:.=sqrt(2*3*3*a*a) xx 4sqrt(3*a*a)$

$color(red)(Note:$

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

$:.=3asqrt2 xx 4*asqrt3$

$:.=12a^2sqrt2 xx sqrt3$

$:.=12a^2sqrt(2*3)$

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

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Simplify $\sqrt{18 a^{2}} \times 4 \sqrt{3 a^{2}}$ $sqrt(18a^2)xx4sqrt(3a^2)$ ?

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Simplify $\sqrt{18 a^{2}} \times 4 \sqrt{3 a^{2}}$ $sqrt(18a^2)xx4sqrt(3a^2)$ ?