Exercise 4 Page 182

We can simplify the given expression by combining like terms. Recall the definition of the imaginary unit i. sqrt(-1)=iLet's begin by rewriting the roots that have a negative radicand as imaginary numbers.

3sqrt(- 24) * 2sqrt(- 18)

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Simplify

SplitIntoFactors

Split into factors

3sqrt(- 1* 24) * 2sqrt(- 1 * 18)

SqrtProd

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

3 sqrt(- 1)* sqrt(24) * 2sqrt(- 1) * sqrt(18)

SqrtNegOneToI

sqrt(- 1)= i

3 i* sqrt(24) * 2isqrt(18)

CommutativePropMult

Commutative Property of Multiplication

3 * 2 * i * i * sqrt(24) * sqrt(18)

Multiply

6i^2 * sqrt(24)* sqrt(18)

IDefPow

i^2=- 1

6(- 1)* sqrt(24)* sqrt(18)

MultPosNeg

a(- b)=- a * b

- 6* sqrt(24)* sqrt(18)

ProdSqrt

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

- 6* sqrt(24* 18)

Multiply

- 6 sqrt(432)

Now we can simplify the square root.

- 6 sqrt(432)

SplitIntoFactors

Split into factors

- 6 sqrt(144 * 3)

SqrtProd

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

- 6 sqrt(144) * sqrt(3)

CalcRoot

Calculate root

- 6 (12) * sqrt(3)

Multiply

- 72sqrt(3)

Hints

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