# CLASSIFYING THE GIVEN RADICAL AS REAL OR IMAGINARY

An imaginary number is the square root of a negative number and does not have a tangible value. While it is not a real number that is, it cannot be quantified on the number line.

Imaginary numbers are "real" in the sense that they exist and are used in math.

The real numbers will not have negative sign inside the square root sign.

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.

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