SOLUTION: the square root of 24 in the simplest radical form

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Question 575188: the square root of 24 in the simplest radical form
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

sqrt%2824%29 Start with the given expression



The goal of simplifying expressions with square roots is to factor the radicand into a product of two numbers. One of these two numbers must be a perfect square. When you take the square root of this perfect square, you will get a rational number.


So let's list the factors of 24


Factors:
1, 2, 3, 4, 6, 8, 12, 24


Notice how 4 is the largest perfect square, so lets factor 24 into 4*6


sqrt%284%2A6%29 Factor 24 into 4*6

sqrt%284%29%2Asqrt%286%29 Break up the square roots using the identity sqrt%28x%2Ay%29=sqrt%28x%29%2Asqrt%28y%29

2%2Asqrt%286%29 Take the square root of the perfect square 4 to get 2

So the expression sqrt%2824%29 simplifies to 2%2Asqrt%286%29

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Check:
Notice if we evaluate the square root of 24 with a calculator we get

sqrt%2824%29=4.89897948556636

and if we evaluate 2%2Asqrt%286%29 we get

2%2Asqrt%286%29=4.89897948556636

This shows that sqrt%2824%29=2%2Asqrt%286%29. So this verifies our answer