Question

What is the square root of 64y16

Answer 1

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

Answer 2

Answer:

Step-by-step 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

$8y^8$