to simplify the root of 84
i understand the steps but im confused as to do you break the 84 as much as you can for example would it be 2 and 42
or28 and 3
21 and 4
so on ...which one do you choose whats the rule I am supposed to follow to figure out the whole answer

Question

to simplify  the root of 84
 i understand the steps but im confused as to do you break the 84 as much as you can for example would it be 2 and 42
or28 and 3
21 and 4 
so on ...which one do you choose whats the rule I am  supposed to follow to figure out the whole answer

unklerhaukus · Answer

om so break up into as small bits as you can (ie factorize the number into primes)

anonymous · Answer

my way I look for the greatest perfect square number that is a factor of the given number

anonymous · Answer

greatest as in this case 2 x 42?

unklerhaukus · Answer

$$\sqrt(84)$$
$$=\sqrt{(2^2\times3\times 7)}$$

mathteacher1729 · Answer

Keep going until you're left with primes. :) 

So 84 = 2*42 
And 
2*42 = 2*2*21
and 
2*2*21 = 2*2*7*3

And we can go no further. 

Now sqrt (2*2*7*3) is really sqrt(2^2) times sqrt(7*3)

BUT... sqrt*2^2) = sqrt(4) = 2
and 
sqrt(7*3) = ... well, we can't simplify that. no "number times itself" under the sqrt. 

So the final simplified answer is just

4 times sqrt(21). 

hope this helps. :)

anonymous · Answer

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