Combine if possible. Do not use a calculator or a table of square roots.(College Algebra-Radicals.)

Question

 Combine if possible. Do not use a calculator or a table of square roots.

 

 

 

-√2 + √32 +√72 =

Answer 1

-√2 + √32 +√72 =-√2 +√16*√2 + √2 * √36

√2*(-1+4+6) = 9*√2

and finally you can solve this knowing by heart the term √2

 

Answer 2

Hey Laura,

 

The key to solving this problem is understanding that you can separate a square root into pieces.  For example sqrt(6) = sqrt(3*2) = sqrt(3)sqrt(2).

 

Since we want to combine these, we want to get a sqrt(2) out of sqrt(32) and sqrt(72).  

 

sqrt(32) = sqrt(16*2) = sqrt(16)*sqrt(2) = 4*sqrt(2)

 

So looking at the first two terms, we have -sqrt(2) + 4*sqrt(2) = 3*sqrt(2)

 

Try using that same reasoning on the sqrt(72) term to see if you can finish it up.  Let me know if you have any more questions!