Question #02059

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Answer 1 · 2017-09-21T23:51:25

#3sqrt(2) = 4.24264068712#

The number 18 can be written as #9*2#. Thus #sqrt(18) = sqrt(9*2)#.

#sqrt(9*2)# can also be writted as #sqrt(9) * sqrt(2)#, and since #sqrt(9) = 3#, #sqrt(18) = 3*sqrt(2) = 3sqrt(2)#.

Answer 2 · 2017-09-22T00:00:00

#3sqrt(2)#

The square root of 18 is an irrational number so it is common to express this in the form #asqrt(b)#. This is known as a simplified surd.

For #sqrt(18)# notice we can factor the number inside the radical ( this is properly called the radicand):

So #sqrt(18) => sqrt( 2 xx 9)#

Since 9 is an exact square we can extract the root and put the root before the radical.

#3sqrt(2)#

The root of 2 is irrational so we leave it.