Question

What is the simplest form of the quotient 4 sqrt 810 / 4 sqrt 2

Answer 1

3 4 sqrt 5

I do not know the explanation but that is the correct answer just took it

Answer 2

`\boxed{3\sqrt[4]{5}}`

Explanation:

The given quotient is

`\frac{\sqrt[4]{810} }{\sqrt[4]{2} }`

We write one radical for the quotient to obtain;

`=\sqrt[4]{(810)/(2) }`

We simplify the radicand (the expression under the radical sign) to obtain;

`=\sqrt[4]{405}`

Find the the prime factorization of the simplified radicand to get;

`=\sqrt[4]{3^4* 5}`

We now split the radical to get;

`=\sqrt[4]{3^4}* \sqrt[4]{5}`

This finally simplifies to;

`=3\sqrt[4]{5}`