How do you simplify $sqrt(24x)*sqrt(6x)$ ?

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Answer 1 · 2018-05-19T11:33:27

$12x$

Given: $sqrt(24x)xxsqrt(6x)$

Note that 24 is the same as $4xx6 -> 2^2xx6$

So if we 'split up' the roots we have:

$color(white)("ddddddd")sqrt(2^2)xxsqrt(6)xx sqrt(x)xxsqrt(6)xxsqrt(x)$

Grouping the values:

$color(white)(dddddd"d") sqrt(2^2)xxubrace(sqrt(6)xxsqrt(6))xx ubrace(sqrt(x)xxsqrt(x))$

$color(white)(dddddd"ddd")ubrace(2color(white)("ddddd")xx6color(white)("dddddd")xx x)$

$color(white)(dddddd"ddddddddddd")12x$

Answer 2 · 2018-05-19T19:18:52

$12x$

$sqrt(24x)*sqrt(6x)$

$:.=sqrt(2*2*2*3x)*sqrt(6x)$

$sqrt2*sqrt2=2$

$:.=2sqrt(6x)*sqrt(6x)$

$:.=sqrt6x*sqrt6x=6x$

$:.=2*6x$

$:.=12x$

How do you simplify sqrt(24x)*sqrt(6x)sqrt(24x)*sqrt(6x)?