Question

What is the exact value for the expression the square root of 189. − the square root of 21. + the square root of 84.? Simplify if possible.

Answer 1

√189-√21+√84

√(3*3*3*7)-√(3*7)+√(2*2*3*7) now if you remove the perfect squares...

3√21-√21+2√21

(3-1+2)√21

4√21

Answer 2

the exact value of the given expression is:
`4√(21)`

Explanation:

we are given to find the value of the expression

square root of 189-square root of 21+square root of 84

`√(189) =√(3*3*3*7)`

`√(189)=3√(21)`

similarly
`√(84)=√(2*2*3*7)=2√(21)`

therefore
`√(189) -√(21)+√(84) =3√(21)-√(21)+2√(21)`

`=4√(21)`

hence the resultant answer corresponding to the given expression is
`4√(21)`.