How do you evaluate 3√8 + 4√50?

1 Answer
Nov 8, 2015

Answer:

  • Check for factors that are quadratic numbers inside the roots
  • Try to make the square roots the same, i.e. #sqrt(3)# or #sqrt(2)#
  • Add them together if the square roots have the same value
    The answer will be #26sqrt(2)#

Explanation:

Let's factorize the numbers inside the square roots.
#3 sqrt(8) + 4 sqrt(50)#
#3 sqrt(2*2*2) + 4sqrt(2*5*5)#

We can see that we have common factors, let's isolate them!
Working with square roots, we can separate factors in the same square root:
#sqrt(ab) = sqrt(a) * sqrt(b)#
Let's do this with our common factors.
(NOTE: We only want TWO common factors as long as we have a square root).

#3 sqrt(2 * 2) * sqrt(2) + 4sqrt(5 * 5) * sqrt(2)#
#3 sqrt(4) * sqrt(2) + 4sqrt(25) * sqrt(2)#

We already know that #sqrt(4) = 2# and #sqrt(25) = 5#, so let's simplify what we have.

#3 * 2 sqrt(2) + 4 * 5 sqrt(2)#
#6 sqrt(2) + 20sqrt(2)#
#26 sqrt(2)#

I hope this helped :-)