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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

3. Simplifying Radical Expressions

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Exercise 54 Page 249

Start by translating the verbal expression into an algebraic expression.

Number: 5
Example Formula: y=1/sqrt(4(x-4))

Practice makes perfect

Given the operations that Marge performs to get 12, we will find the number with which she started. Let's first express the given operations as algebraic expressions and then write a formula.

Verbal Expression	Algebraic Expression
Starting Number	x
Subtract 4	x- 4
Multiply by 4	4( x- 4)
Take the Square Root	sqrt(4( x- 4))
Take the Reciprocal	1/sqrt(4( x- 4))
Get 1/2	1/sqrt(4( x- 4))= 1/2

We need to solve this equation for x to find the number with which she started. To do so, we will use inverse operations and Properties of Equality. Let's start by applying the Cross Products.

1/2=1/sqrt(4(x-4))

▼

Solve for x

Cross multiply

sqrt(4(x-4))=2

LHS^2=RHS^2

(sqrt(4(x-4)))^2=4

( sqrt(a) )^2 = a

4(x-4)=4

Distribute 4

4x-16=4

LHS+16=RHS+16

4x=20

.LHS /4.=.RHS /4.

x=5

Therefore, the number that Marge started with is 5. Finally, to write the formula, let y be any number we want to get it. By substituting y for 12 into the equation, we will have a formula which can be used to find any output given an input or any input given an output when following this procedure. y=1/sqrt(4(x-4))

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Exercises p.248-250