How do you express #-5sqrt40# in simplest radical form?

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Answer 1 · 2018-08-05T04:03:39

#" "#
The radical expression given #color(red)(-5 sqrt(40)# can be written in simplest form as #color(blue)([-10 sqrt(10)]#

#" "#
Given:

#color(red)(-5 sqrt(40)#

#rArr -5*sqrt(8*5)#

#rArr -5*sqrt(4*2*5)#

#rArr =5*sqrt(4)*sqrt(10)#

#rArr -5*2*sqrt(10)#

#rArr -10*sqrt(10)#

Hence, the radical expression given #color(red)([-5 sqrt(40)]# cn be written in simplest form as #color(blue)([-10 sqrt(10)]#

Hope it helps.

Answer 2 · 2018-08-06T02:45:53

#-10sqrt10#

Since #40=4*10#, we can rewrite #sqrt40# as #sqrt4sqrt10#. We now have

#-5sqrt4sqrt10#

Recall that #sqrt4=2#. With this simplification, we now have

#-10sqrt10#

Since the radical has no perfect square factors, this is the most we can simplify this.

Hope this helps!