radicals

[ali1]

When 5 radical 20 is written in simplest form, the result is k radical 5. What is the value of k?

 

[masters]

When 5 radical 20 is written in simplest form, the result is k radical 5. What is the value of k?

Hi ali1,

Simplify: \(\displaystyle 5\sqrt{20}\)

We want to factor out the largest perfect square factor of the radicand, if it has one.

Fortunately, this one has one. The radicand (20) can be factored into 4 times 5.

Now let's restate it this way:

\(\displaystyle 5\sqrt{4\cdot 5}\)

This way, we can extract the square root of 4 and bring it to the outside of the radical and leave the 5 inside.

\(\displaystyle 5\cdot 2\sqrt{5}\)

Looks like your value of k is intuitively obvious to the most casual observer.

 

[mmm4444bot]

First, you need to be able to simplify radicals.

Do you know how to simplify \(\displaystyle \sqrt{20}\) ?