`sqrt(a^(16)b)` How to solve it?  When is `sqrt(y)`not defined in the real number system? `` a) when y < 0 b) when y > 0 c) when y `>=0` d) when y`<=0`

Expert Answers
lemjay eNotes educator| Certified Educator

(I)` sqrt(a^16b)`

To simplify this, take the square root of each factor.

`=sqrt(a^16) * sqrtb`

Since the index of the radical is 2, a factor that has an even number exponent can be simplified. It can be simplified by dividing its exponent by 2.

`=a^(16/2)*sqrtb`

`=a^8sqrtb`

Hence, the simplified form is `sqrt(a^16b)=a^8sqrtb` .

(II) `sqrt(y)`

The index of this radical is 2.

When the index is an even number, the radicand should be zero and above. Negative numbers are not allowed inside the radical symbol.

Therefore, `sqrt(y)` is not defined in the real number system when y<0.