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Big Ideas Math Integrated II

BI

Big Ideas Math Integrated II View details

Chapter Review

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Exercise 1 Page 268

Remember that sqrt(a* b)=sqrt(a)*sqrt(b).

6p^3sqrt(2p)

Practice makes perfect

We can simplify this expression by rewriting the number under the square root as the product of at least one perfect square factor.

sqrt(72p^7)

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Split into factors

Rewrite 72 as 9* 8

sqrt(9* 8* p^7)

Rewrite 8 as 4* 2

sqrt(9* 4* 2* p^7)

Rewrite p^7 as p^6* p

sqrt(9* 4* 2* p^6* p)

Rewrite p^6 as p^2* p^2* p^2

sqrt(9* 4* 2* p^2* p^2* p^2* p)

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

sqrt(9)*sqrt(4)*sqrt(2)*sqrt(p^2)*sqrt(p^2)*sqrt(p^2)*sqrt(p)

Calculate root

3* 2*sqrt(2)*sqrt(p^2)*sqrt(p^2)*sqrt(p^2)*sqrt(p)

SqrtPowToNumber

sqrt(a^2)=a

3* 2*sqrt(2)* p* p* p*sqrt(p)

▼

Multiply

ProdToPowThreeFac

a* a* a=a^3

3* 2*sqrt(2)* p^3*sqrt(p)

Multiply

6p^3*sqrt(2)*sqrt(p)

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

6p^3sqrt(2p)

Remember that we assume that the variable p is positive.

Subchapter links

1 Properties of Radicals p.268

2 Solving Quadratic Equations by Graphing p.268

3 Solving Quadratic Equations Using Square Roots p.269

4 Solving Quadratic Equations by Completing the Square p.269

5 Solving Quadratic Equations Using the Quadratic Formula p.270

6 Complex Numbers p.270

7 Solving Quadratic Equations with Complex Solutions p.271

8 Solving Nonlinear Systems of Equations p.272

9 Quadratic Inequalities p.272