# `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`

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Expert Answers

lemjay | 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.**