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Coolmath Algebra
Radicals lesson 4 - Adding & Subtracting Radicals   (page 1 of 1)
---- This algebra lesson explains how to add and subtract radicals.

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This game goes along with the game in the last section.  Yes, it's definitely a pre-calculator thing...  But, it's on a lot of standardized math tests...  So, here we go!

We want to add these guys without using decimals:

sqrt(2) + sqrt(8)

The game is to simplify everyone and see if we can combine anything.

sqrt(2) is already done.

sqrt(8) = sqrt(4*2) = ( sqrt(4) )( sqrt(2) ) = 2 * sqrt(2)

 

So, sqrt(2) + sqrt(8) = sqrt(2) + 2 * sqrt(2)

Now, we treat the radicals like variables.  Think of it as

y + 2y = 3y
 

sqrt(2) + sqrt(8) = sqrt(2) + 2*sqrt(2) = 3*sqrt(2)

Done!

Here's another one:

sqrt(48) - sqrt(3) + sqrt(75)

Rewrite the radicals...

sqrt(48) - sqrt(3) + sqrt(75) = sqrt(16*3) - sqrt(3) + sqrt(25*3) = 4*sqrt(3) - sqrt(3) + 5*sqrt(3) = 8*sqrt(3)

(Do it like  4x - x + 5x = 8x. )

YOUR TURN:

sqrt(45) + sqrt(20) +sqrt(5) - sqrt(125)

CRUNCH SOME: Click here to get some practice problems

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