`sqrt(75/36)` Simplify the expression.

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chrisyhsun | Student, College Freshman | (Level 1) Salutatorian

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The first thing I would do for this type of problem is see if the inner fraction can be simplified. Since it can't in this case, we will simply break down the problem into two smaller issues - the numerator and the denominator.

For the numerator, we are trying to figure out the square root of 75. The best advice I have for this is to take the prime factorization of 75 and see which factors get "paired up" (aka can be taken out from under the square root symbol). In this case, the prime factorization is 5*5*3, which means 5 gets taken out and 3 stays under the root symbol.

Next, let's take a look at the denominator. The same method of finding the prime factorization then taking out the pairs would certainly work in this case (36 = 2*2*3*3, take out a 2, take out a 3, and multiply). However, the fastest way is to memorize the squares (until about 15, I would say). For this case, you don't even need the squares up that high to know that 36 is 6 squared. Therefore, the denominator (square root of 36) can be simplified down to 6.

Putting the numerator and the denominator together, we get that the final answer is (5 root 3) / 6, which cannot be further simplified because 5 and 6 don't share common factors besides 1.