Question

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

Answer 1

Answer:

3 4 sqrt 5

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

Answer 2

Answer:

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

Step-by-step explanation:

The given quotient is

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

We write one radical for the quotient to obtain;

$=\sqrt[4]{\frac{810}{2} }$

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;

$=\sqrt[4]{3^4\times 5}$

We now split the radical to get;

$=\sqrt[4]{3^4}\times \sqrt[4]{5}$

This finally simplifies to;

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