How do you completely simplify #sqrt(3m) * sqrt(8m)#?

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Answer 1 · 2017-04-24T20:30:10

See the solution process below:

We can use this rule to first combine the terms:

#sqrt(a) * sqrt(b) = sqrt(a * b)#

#sqrt(3m) * sqrt(8m) = sqrt(3m * 8m) = sqrt(24m^2)#

We can use this same rule to again rewrite the expression as:

#sqrt(24m^2) = sqrt(24) * sqrt(m^2) = sqrt(24)m#

We can continue to simplify by using this rule to again rewrite the expression as:

#sqrt(24)m = sqrt(6 * 4)m = sqrt(6) * sqrt(4)m = +-2msqrt(6)#

If we want to take the #sqrt(6)# it is #2.4449# rounded to the nearest thousandth and:

#+-2msqrt(6) = +-2m * 2.449 = +-4.898m# rounded to the nearest thousandth.