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

3 Answers
salamat
Mar 29, 2017

= 12 a^2 sqrt6

Explanation:

sqrt(18a^2) * 4 sqrt(3a^2) = 4 sqrt(18a^2 *3a^2)

= 4 sqrt(54a^4) = 4 sqrt(9 a^4 * 6)

= 4 sqrt(9 a^4) * sqrt 6

= 4 * 3a^2 * sqrt 6

= 12 a^2 sqrt6

Tony B
Mar 29, 2017

12a^2sqrt(6)

Explanation:

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

Given:" "sqrt(18a^2)xx4sqrt(3a^2)

We can 'extract' the a^2 giving:

asqrt(18)xx4asqrt(3)

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

Note that 18->2xx9->2xx3^2 giving:

asqrt(2xx3^2)xx4asqrt(3)

We can 'extract' the 3^2

3asqrt(2)xx4asqrt(3)

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

Combining the contents of the roots.

3axx4axxsqrt(2xx3)

12a^2sqrt(6)

Barney V.
Mar 29, 2017

color(red)(12a^2sqrt6

Explanation:

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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