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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))

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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

CrossMult

Cross multiply

sqrt(4(x-4))=2

RaiseEqn

LHS^2=RHS^2

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

PowSqrt

( sqrt(a) )^2 = a

4(x-4)=4

Distr

Distribute 4

4x-16=4

AddEqn

LHS+16=RHS+16

4x=20

DivEqn

.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

Exercise 54 Page 249

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