How do you simplify #sqrt(250a^2) + sqrt(10a^2)#?

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Answer 1 · 2015-05-07T07:12:16

Let's look at the two terms individually first:

#color(red)(sqrt(250a^2)) = sqrt (25*10 *a^2) #

# = sqrt 25*sqrt 10*sqrt(a^2)# Because #color(blue)(sqrt(ab) = sqrt a * sqrt b#

# = 5*sqrt10*a = color(red)(5asqrt10#

#color(green)(sqrt(10a^2)) = sqrt10 * sqrt(a^2) = color(green)(asqrt10#

Hence
#color(purple)(sqrt(250a^2) + sqrt(10a^2)) = 5asqrt10 + asqrt10#

#sqrt10# is common to both the terms

# = sqrt10(5a + a)#

# = sqrt10(6a)#

# = color(purple)(6asqrt10#