Exercise 55 Page 197

We can simplify the given expression by combining like terms. Recall the definition of the imaginary unit i. sqrt(-1)=i and -1=i^2Let's begin by rewriting the roots that have a negative radicand as imaginary numbers.

4sqrt(- 9)* 2sqrt(- 25)

SplitIntoFactors

Split into factors

4sqrt(- 1* 9)* 2sqrt(- 1* 25)

SqrtProd

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

4sqrt(- 1)*sqrt(9)* 2sqrt(- 1)*sqrt(25)

SqrtNegOneToI

sqrt(- 1)= i

4i*sqrt(9)* 2i* sqrt(25)

CalcRoot

Calculate root

4i* 3* 2i* 5

Now we can multiply the terms.

4i* 3* 2i* 5

Multiply

Multiply

120i^2

IDefPow

i^2=- 1

120(- 1)

MultPosNeg

a(- b)=- a * b

- 120