Question #19389

1 Answer
SoySoy4444
Dec 1, 2017

#-2sqrt(15)#

Explanation:

Let's first think of the positive square root of #60#. First of all, I hope you know that #60# isn't a perfect square. Therefore, we get this: #sqrt(60)#. However, we can simplify this. What we do is as follows:

  1. We look for its factors. They are #1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60#
  2. We look for the highest perfect square in the factors, if it exists. We find that it is #4#.
  3. We rewrite the square root as a product of the highest square number (In this case, #4#) and its other factor (In this case, #15#.)
    This would give us #sqrt(4*15)#.
  4. Now we square root out the perfect square. Since the square root of #4# is #2#, we get: #2sqrt(15)#

However, we want the negative square root of that. Just simply multiply that by #-1#: #-2sqrt(15)#

And that is your answer.

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