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

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) (Show Source): You can put this solution on YOUR website!
Start with the given expression

Combine the roots using the identity

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 ), so lets factor 450 into 225*2

Factor 450 into 225*2

Break up the square roots using the identity

Take the square root of the perfect square 225 to get 15

So the expression simplifies to

This consequently means that simplifies to as well

===========================================

Answer:

So

RELATED QUESTIONS
Please help me simplify this radical expression: Simplify the radical expression of a... (answered by rothauserc)

please help me simplify this expression 5 square root r times square root... (answered by user_dude2008)

Can someone please help me with this: Simplify the expression. 3(square root)8... (answered by jim_thompson5910)

I have been working on this math problem and I can't figure out how to get the answer. I... (answered by nerdybill)

Please help me simplify this radical. 3 Square root 6 minus 3 square root... (answered by jim_thompson5910)

How would you simplify the square root of... (answered by ewatrrr)

Please help me simplify this expression: the square root of... (answered by edjones)

how do I simplify square root-6 square root-42 I know I divide 6 into 42 so would this... (answered by Fombitz)

how do you simplify the square root of 3 over the square root of... (answered by Alan3354)