How do you evaluate square root of 32a^8b + square root of 50a^16b?

1 Answer
George C.
Dec 31, 2015

Use properties of square root of products to find:

#sqrt(32a^8b)+sqrt(50a^16b)=a^4(4+5a^4)sqrt(2b)#

Explanation:

If #x >= 0# or #y >= 0#, then #sqrt(xy) = sqrt(x)sqrt(y)#

(Note this does not hold if both #x < 0# and #y < 0#)

So we find:

#sqrt(32a^8b)+sqrt(50a^16b)#

#=sqrt(16a^8)sqrt(2b)+sqrt(25a^16)sqrt(2b)#

#=sqrt((4a^4)^2)sqrt(2b)+sqrt((5a^8)^2)sqrt(2b)#

#=(4a^4 + 5 a^8)sqrt(2b)#

#=a^4(4+5a^4)sqrt(2b)#

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