SOLUTION: Simplify the expression. Square root 75 * square root 6 How would you simplify this? Please help!

Algebra ->  Radicals -> SOLUTION: Simplify the expression. Square root 75 * square root 6 How would you simplify this? Please help!      Log On


   

Question 189994This question is from textbook Saxon Algebra 2
: Simplify the expression.
Square root 75 * square root 6
How would you simplify this? Please help! This question is from textbook Saxon Algebra 2

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%2875%29%2Asqrt%286%29 Start with the given expression


sqrt%2875%2A6%29 Combine the roots using the identity sqrt%28x%29%2Asqrt%28y%29=sqrt%28x%2Ay%29


sqrt%28450%29 Multiply


Now 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 450


Factors:
1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, 450


Notice how 225 is the largest perfect square (since 15%5E2=225), so lets factor 450 into 225*2


sqrt%28225%2A2%29 Factor 450 into 225*2



sqrt%28225%29%2Asqrt%282%29 Break up the square roots using the identity sqrt%28x%2Ay%29=sqrt%28x%29%2Asqrt%28y%29



15%2Asqrt%282%29 Take the square root of the perfect square 225 to get 15



So the expression sqrt%28450%29 simplifies to 15%2Asqrt%282%29



This consequently means that sqrt%2875%29%2Asqrt%286%29 simplifies to 15%2Asqrt%282%29 as well

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Answer:

So sqrt%2875%29%2Asqrt%286%29=15%2Asqrt%282%29