What is the square root of 24?

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Answer 1 · 2018-03-24T05:36:10

#2sqrt(6)#

Given: #sqrt(24)#

We split it into the following:

#=sqrt(4*6)#

Now, we use the radical rule which states that, #sqrt(ab)=sqrt(a)*sqrt(b),a,b>0#.

So, we get,

#=sqrt(4)*sqrt(6)#

#=2sqrt(6)#

Answer 2 · 2018-03-24T05:37:03

#sqrt(24)=2sqrt(6)#

We should try to reduce #sqrt(24)# to the root of a number with a perfect square multiplied by some other whole number.

Let's consider the factors of #24:#

#1, 4, 6, 8, 12, 24#

Out of these, #4# is the largest (and coincidentally, only) perfect square present.

#4*6=24,# so we can rewrite as

#sqrt(24)=sqrt(4*6)=sqrt(4)*sqrt(6)# as #sqrt(ab)=sqrt(a)*sqrt(b)#

Simplify:

#sqrt(4)*sqrt(6)=2sqrt(6)#