Question

How do you simplify `sqrt(84)`?

Answer 1

2√21

Explanation:

√84=√4*21 = 2√21

Always check if the number inside the root can be broken down into a perfect square which is also must be a factor. then write as √4*21 then take out the 4. when it is taken out '4', factors out and becomes 2 as in 2√21. this can be done until no perfect squares are left inside the root.

Answer 2

`2sqrt21`

Explanation:

To simplify a radical write in the form `asqrtb`

To obtain this form : consider the factors of 84 ,finding if possible one which is a perfect square.

in this case: 84 = 4 `xx 21 and so sqrt84 = sqrt(4 xx 21)`

using `sqrt(ab) = sqrta xx sqrtb rArr sqrt(4 xx 21) =sqrt4 xx sqrt21`

21 cannot be simplified any further as it's factors are all prime and so

`sqrt84 = sqrt4 xx sqrt21 = 2sqrt21`