SOLUTION: Use property 1 to simplify each of the radical expressions. Assume that all variables represent positive real numbers. 1. square root of 50 2. square root of 72x cubed

Question 118059: Use property 1 to simplify each of the radical expressions. Assume that all variables represent positive real numbers.
1. square root of 50
2. square root of 72x cubed
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
#1

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 50
Factors:
1, 2, 5, 10, 25, 50

Notice how 25 is the largest perfect square, so lets factor 50 into 25*2

Factor 50 into 25*2

Break up the square roots using the identity

Take the square root of the perfect square 25 to get 5

So the expression simplifies to

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Check:
Notice if we evaluate the square root of 50 with a calculator we get

and if we evaluate we get

This shows that . So this verifies our answer

#2

Start with the given expression
Factor into

Factor into

Break up the square root using the identity

Take the square root of the perfect square to get 6

Take the square root of the perfect squares to get

Rearrange the terms
Group the square root terms

So simplifies to
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