Imaginary Numbers and Square Roots

This lesson teaches how to express the square root of a negative number using the imaginary unit i. It begins by explaining the difference between real and imaginary numbers, focusing on the sign of the number under the radical. The lesson reviews simplifying square roots of positive numbers using prime factors and introduces the imaginary unit i, defined as the square root of negative one. It then demonstrates how to simplify square roots of negative numbers using i, with examples illustrating the process.

What distinguishes a real number from an imaginary number?

• Whether the number is positive or negative

• Whether the number is even or odd

• Whether the number is prime or composite

• Whether the number is a fraction or a whole number

How do you simplify the square root of a positive number?

• By subtracting the number from 100

• By using the number's prime factors

• By dividing the number by 2

• By adding the digits of the number

What is the result of simplifying the square root of 90?

• 9 root 10

• 3 root 9

• 10 root 3

• 3 root 10

What is the imaginary unit 'i' defined as?

• The square root of negative one

• The square root of two

• The square root of 1

• The square root of 0

How is the square root of negative 25 simplified using 'i'?

• i5

• 25i

• i25

• 5i

What is the prime factorization of 72 used in the example?

• 3 x 3 x 3 x 3

• 2 x 2 x 2 x 3

• 2 x 3 x 3 x 3

• 2 x 2 x 3 x 3

How is the square root of negative 72 expressed using 'i'?

• 6 root 2

• 6i root 2

• i root 72

• 72i

What is the square root of 36?

• 8

• 7

• 6

• 5

What is the prime factorization of 14?

• 2 x 7

• 2 x 2 x 7

• 7 x 7

• 2 x 3 x 7

How is the square root of negative 14 expressed using 'i'?

• i root 14

• root 14i

• 14i

• i14