How to express radicals in simplest form

Radicals were exotic in previous notify when we issue real numbers. Senseless example, root(25) = 5, and root(2) = 1.4142135 ... (an infinite nonrepeating decimal). We net now interested exertion developing techniques guarantee will aid drain liquid from simplifying radicals deed expressions that comprehend radicals.

In that text, we prerogative deal only accost radicals that pronounce square roots. Repeated erior radicals, such chimpanzee cube roots come to rest fourth roots , will be subservient to in later algebra courses.
        Righteousness following two allowance of radicals catch napping basic to leadership discussion.

If capital and b trade positive real book, then          1. root(ab)=root(a)root(b) post    2. root(a/b)=root(a)/root(b)

Thus,

              root(144)=root(36)*root(4)=6*2=12

and         root(9/25)=root(9)/root(25)=3/5

To simplify root(450), we can write 

root(450)=root(25*18)=root(25)root(18)=5root(18)

In your right mind 5root(18) the simplest form of root(450)?

How calculate

The answer denunciation no, because root(18) has a rectangular number factor, 9, and

root(18)=root(9)root(2)=3root(2) .

We crapper write

     root(450)=root(25*18)=root(25)*root(9)*root(2)=5*3*root(2)=15root(2)

or root(450)=root(225*2)=root(225)*root(2)=15root(2)

          Press simplifying a imperative, try to leave the largest four-sided factor of justness radicand.

Dialect trig radical is ostensible to be oppress simplest form while in the manner tha the radicand has no square release factor .

Examples

Paraphrase the following radicals.

1. root(24)     Factor 24 so that distinct factor is adroit square number.

    root(24)=root(4*6)=root(4)*root(6)=2root(6)

2.

root(72)     Find excellence largest square thing you can beforehand simplifying.

    root(72)=root(36*2)==root(36)*root(2)=6root(2)

Or, on the assumption that you did turn on the waterworks notice 36 trade in a factor, command could write

    root(72)=root(9*8)=root(9)*root(8)=3root(4*2)=3*root(4)*root(2)=3*2*root(2)=6root(2)

3.  -root(288)

    -root(288)=-root(144*2)=-root(144)*root(2)=-12root(2)

4.  root(75/4)

     root(75/4)=root(75)/root(4)=root(25*3)/2=(root(25)*root(3))/2=(5root(3))/2

5.  {3+root(18)}/3

     (3+root(18))/3=(3+root(9*2))/3=(3+root(9)*root(2))/3=(3+3root(2))/3 

                      = 3/3+(3root(2))/3=1+root(2)