SOLUTION: Enter the simplified form of square root of 75

Algebra ->  Radicals -> SOLUTION: Enter the simplified form of square root of 75      Log On


   

Question 119144: Enter the simplified form of square root of 75
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

sqrt%2875%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 75


Factors:
1, 3, 5, 15, 25, 75


Notice how 25 is the largest perfect square, so lets factor 75 into 25*3


sqrt%2825%2A3%29 Factor 75 into 25*3

sqrt%2825%29%2Asqrt%283%29 Break up the square roots using the identity sqrt%28x%2Ay%29=sqrt%28x%29%2Asqrt%28y%29

5%2Asqrt%283%29 Take the square root of the perfect square 25 to get 5

So the expression sqrt%2875%29 simplifies to 5%2Asqrt%283%29

----------------------------
Check:
Notice if we evaluate the square root of 75 with a calculator we get

sqrt%2875%29=8.66025403784439

and if we evaluate 5%2Asqrt%283%29 we get

5%2Asqrt%283%29=8.66025403784439

This shows that sqrt%2875%29=5%2Asqrt%283%29. So this verifies our answer