body{margin:0;} noscript{z-index: 10000; position: fixed; display: block; height: 100%; width: 100%; background: #fff;} noscript .fa{font-size: 40px; display:block; color: #daa520;} noscript div{margin-top: 6%; padding-left: 20px; padding-right: 20px; text-align: center;} ! You must have JavaScript enabled to use this site.

McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

3. Simplifying Radical Expressions

Continue to next subchapter

Exercise 53 Page 249

Practice makes perfect

a

Let's examine the given expression.

sqrt(27) Notice that this is a cube root expression. To simplify it, we will first split the radicand into prime factors. Then, we will look for perfect cube factors.

sqrt(27)

SplitIntoPrimeFactors

Split into prime factors

sqrt(3*3*3)

ProdToPowThreeFac

a* a* a=a^3

sqrt(3^3)

RootPowToNumber

sqrt(a^3)=a

3

b

In this part, we will also split the radicand into prime factors and look for perfect cube factors. Additionally, we will use the Product Property of Radicals.

sqrt(40)

SplitIntoPrimeFactors

Split into prime factors

sqrt(2*2*2*5)

ProdToPowThreeFac

a* a* a=a^3

sqrt(2^3 *5)

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

sqrt(2^3)* sqrt(5)

RootPowToNumber

sqrt(a^3)=a

2sqrt(5)

c

We will proceed in the same way as Part B to simplify this expression.

sqrt(750)

SplitIntoPrimeFactors

Split into prime factors

sqrt(2*3*5*5*5)

ProdToPowThreeFac

a* a* a=a^3

sqrt(2*3*5^3)

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

sqrt(2*3)* sqrt(5^3)

RootPowToNumber

sqrt(a^3)=a

sqrt(2*3) * 5

CommutativePropMult

Commutative Property of Multiplication

5sqrt(2*3)

Multiply

5sqrt(6)

Subchapter links

Exercises p.248-250