Simplifying √(1)2+(2t)2+(2t2)2= 1+2t2: Understanding the Solution

[Mdhiggenz]

Homework Statement

√(1)²+(2t)²+(2t²)²= 1+2t²

I'm a bit confused I'm getting √(1+4t^2+4t^2) don't quite understand how they are getting the above answer.

Thanks

Homework Equations

The Attempt at a Solution

 

[LCKurtz]

Homework Statement

√(1)²+(2t)²+(2t²)²= 1+2t²

I'm a bit confused I'm getting √(1+4t^2+4t^2) don't quite understand how they are getting the above answer.

Thanks

An algebra mistake:$\sqrt{1+(2t)^2+(2t^2)^2}=\sqrt{1+4t^2+4t^4}$ Does that help?

 

[Mdhiggenz]

No, that was a typo on my part. I originally got the same thing as you. If you factor out a 4t^2

You get √1+4t^2(1+t^2). I don't see how anything can be canceled due to that pesky 1 term.

 

[Curious3141]

No, that was a typo on my part. I originally got the same thing as you. If you factor out a 4t^2

You get √1+4t^2(1+t^2). I don't see how anything can be canceled due to that pesky 1 term.

There's no cancellation here. You're merely simplifying the left hand side to get the right hand side.

What is ${(1 + 2t^2)}^2$?

 

[Mdhiggenz]

Haha wow silly me. This has always actually confused me, is there a set formula to condense it the way you did?

Thanks again for the help

 

[Curious3141]

Haha wow silly me. This has always actually confused me, is there a set formula to condense it the way you did?

Thanks again for the help

No, just observation of the form $a^2 + 2ab + b^2$. I guess it comes with experience and practice.