Question

What is the square root of 64y16

Answer 1

Explanation:

The idea here is to "match" the exponent on the radicands (the number/variables under the radical sign) to the index (the little number that sits in the "arm" of the radical sign). Your problem looks like this:

`\sqrt[2]{64y^(16)}`

Our index is a 2. If we could rewrite both the 64 and the y^16 with bases to the power of 2 (that's why I say to "match" the exponent to the index), we could pull out the base. For example,

`\sqrt[2]{x^2}=x` because the power is a 2 and so is the index, so we pull out the base of x.

Our rewrite would look like this:

`\sqrt[2]{8^2(y^8)^2}` (remember that power to power on a base means you multiply the exponents so 8 * 2 = 16).

The power on the 8 is a 2 which matches our index of 2 so we will pull out the 8; the power on the y^8 is a 2 which also matches our index of 2 so we will pull out the y^8. The simplification of this is

`8y^8`

Answer 2

The answer to the square root of 64y16 is 8y8.