CLASSIFYING THE GIVEN RADICAL AS REAL OR IMAGINARY

Identify each as Real (R) or Imaginary (C). Then simplify.

Problem 1 :

√49

Solution :

√49

√49 = √(7 × 7)

= 7

So, √49 is real term.

Problem 2 :

√-49

Solution :

√-49

Square root of a negative number is considered to be an imaginary value.

= √49 × √-1

= √(7 × 7) × √-1

= 7i

So, √-49 is imaginary term.

Problem 3 :

√16

Solution :

√16

√16 = √(4 × 4)

= 4

So, √16 is real term.

Problem 4 :

√-25

Solution :

√-25

Square root of a negative number is considered to be an imaginary value.

= √25 × √-1

= √(5 × 5) × √-1

= 5i

So, √-25 is imaginary term.

Problem 5 :

√-81

Solution :

√-81

Square root of a negative number is considered to be an imaginary value.

= √81 × √-1

= √(9 × 9) × √-1

= 9i

So, √-81 is imaginary term.