Can you show me, step-by-step and in the simplest terms possible, how to solve 2√8 + 6√50?

Question

I have a very hard time with radical problems and I'd appreciate some help...

Answer 1

Alright, Victoria, let's make this easier.

 

So, we can break down what's under the radical into factors.

 

√8 = √(4(2)) = √4√2

 

What's the square root of 4? 2. We already have a 2 in front of 2√8, so...

 

 

2√8 = 2(2)√2 = 4√2

 

6√50 = 6√(25(2)) = 6√25√2 = 6(5)√2 = 30√2

 

Now, just like 4x + 30x = 34x...

 

4√2 + 30√2 = 34√2

 

Hope this helps!

Answer 2

"solve" is not exactly the correct word here (we solve equations); what we do here is to simplify radical expressions.

 

It's easy; just rewrite every radicand after factoring it so that as many factors as possible are perfect squares.

 

square root of eight is square root of (4•2) and that yields 2√2.

square root of fifty is square root of (25•2) and that yields 5√2.

Thus your final answer is 34√2.