ali1

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

masters

Full Member
ali1 said:
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

Super Moderator
Staff member
First, you need to be able to simplify radicals.

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