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radicals

ali1

New member
Joined
Jan 27, 2010
Messages
1
When 5 radical 20 is written in simplest form, the result is k radical 5. What is the value of k?
 

masters

Full Member
Joined
Mar 30, 2007
Messages
378
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
Joined
Oct 6, 2005
Messages
10,158
First, you need to be able to simplify radicals.

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