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McGraw Hill Integrated II, 2012

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McGraw Hill Integrated II, 2012 View details

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Exercise 6 Page 617

Start by rationalizing the denominator.

- 4sqrt(2)+8/3

Practice makes perfect

Consider the given expression. 8sqrt(2)/6-3sqrt(8)

To simplify it, we need to rationalize the denominator. To do so, we have to multiply the numerator and denominator of the fraction by the conjugate of the denominator. We find the conjugate by changing the sign of the second term of the expression.

Binomial	Conjugate
a + b	a - b
a - b	a + b

In this case, the conjugate of the denominator is 6 + 3sqrt(8). Let's rationalize the denominator and then simplify the expression.

8sqrt(2)/6-3sqrt(8)

a/b=a * (6+3sqrt(8))/b * (6+3sqrt(8))

8sqrt(2)(6+3sqrt(8))/(6-3sqrt(8))(6+3sqrt(8))

▼

Multiply parentheses

Distribute 8sqrt(2)

48sqrt(2)+24sqrt(2)sqrt(8)/(6-3sqrt(8))(6+3sqrt(8))

sqrt(a)*sqrt(b)=sqrt(a* b)

48sqrt(2)+24sqrt(16)/(6-3sqrt(8))(6+3sqrt(8))

Calculate root

48sqrt(2)+24 * 4/(6-3sqrt(8))(6+3sqrt(8))

Multiply

48sqrt(2)+96/(6-3sqrt(8))(6+3sqrt(8))

(a-b)(a+b)=a^2-b^2

48sqrt(2)+96/6^2-(3sqrt(8))^2

▼

Simplify denominator

a^m b^m = (a b)^m

48sqrt(2)+96/6^2-3^2(sqrt(8))^2

Calculate power

48sqrt(2)+96/36-9(sqrt(8))^2

( sqrt(a) )^2 = a

48sqrt(2)+96/36-9 * 8

Multiply

48sqrt(2)+96/36-72

Subtract term

48sqrt(2)+96/- 36

Factor out 12

12(4sqrt(2)+8)/- 36

a/b=.a /12./.b /12.

4sqrt(2)+8/- 3

MoveNegDenomToFrac

Put minus sign in front of fraction

- 4sqrt(2)+8/3

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