Exercise 29 Page 266

To simplify the given expression, use perfect squares to group radicals with like radicands.

-2sqrt(6)+11sqrt(3)

Practice makes perfect

Radicals can only be added or subtracted when they have like radicands. a sqrt(x) + b sqrt(x) = (a+b) sqrt(x) asqrt(x)-bsqrt(x)=(a-b)sqrt(x)Let's use perfect squares to simplify our radicals to see if we can create like terms.

sqrt(6)-sqrt(54)+3sqrt(12)+5sqrt(3)

SplitIntoFactors

Split into factors

sqrt(6)-sqrt(9*6)+3sqrt(4* 3)+5sqrt(3)

SqrtProd

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

sqrt(6)-sqrt(9)*sqrt(6)+3sqrt(4)*sqrt(3)+5sqrt(3)

CalcRoot

Calculate root

sqrt(6)-3* sqrt(6)+3*2*sqrt(3)+5sqrt(3)

Multiply

sqrt(6)-3sqrt(6)+6sqrt(3)+5sqrt(3)

Now we will factor out common factors to perform the addition and subtraction.

sqrt(6)-3sqrt(6)+6sqrt(3)+5sqrt(3)

FactorOut

Factor out sqrt(6)

(1-3)sqrt(6)+6sqrt(3)+5sqrt(3)

SubTerm

Subtract term

-2sqrt(6)+6sqrt(3)+5sqrt(3)

FactorOut

Factor out sqrt(3)

-2sqrt(6)+(6+5)sqrt(3)

AddTerms

Add terms

-2sqrt(6)+11sqrt(3)

Subchapter links

1 Graphing Exponential Functions p.265

2 Solving Exponential Equations and Inequalities p.265

3 Simplifying Radical Expressions p.265

4 Operations with Radical Expressions p.266

5 Radical Equations p.266

Exercise 29 Page 266

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