Question

For which value of x must the expression square root of 19x be further simplified? A. 15. B 21. C 28. D 41

Answer 1

The expression of the square root of 19x must be simplified when x is equal to 28. This is because possible factors of 28 can be seen to be 4 and 7, and 4 is a perfect square. This means it can be pulled outside of the square root when evaluated. The other options include only prime factors that could not be pulled out. (3,5), (3,7), (1,41)
28 simplifies as such:
Sqrt(19*28) = Sqrt(19*4*7) = 2*Sqrt(19*7) = 2*Sqrt(133).

Answer 2

C 28

Explanation:

Let:

`f(x)=√(19x)`

Now, let's evaluate every value, so we can determinate if the expression can be further simplified:

`x=15`

`f(15)=√(19*15) =√(285)`

This can't be simplified because it can't be expressed as the product of a series of prime factors raised to the exponent of the root.

`x=21`

`f(21)=√(19*21) =√(399)`

This can't be simplified because it can't be expressed as the product of a series of prime factors raised to the exponent of the root.

`x=28`

`f(28)=√(19*28) =√(532)`

This can be simplified because you can rewrite the expression as:

`√(532) =√(2^2*133) = √(4*133) =√(4) √(133) =2√(133)`

`x=41`

`f(41)=√(19*41) =√(779)`

This can't be simplified because it can't be expressed as the product of a series of prime factors raised to the exponent of the root.