Principal Roots and Irrational Numbers

​Additional Learning Resources

• https://youtu.be/mFVCWcR7H-4​

Multiple Choice

What do you call a number that can be expressed in the form $$\frac{a}{b}$$  , where a and 𝑏 b are integers, and b is not equal to 0?

• Integers

• Irrational

• natural

• rational

Multiple Choice

Which of the following refers to a number whose decimal representation is neither terminating nor repeating? This number cannot be expressed as a quotient of integers.

• Integers

• Irrational

• natural

• rational

Multiple Choice

What do you call the positive $$n^{th}$$   root of a number?

• perfect square

• principal root

• radical

• radicand

Multiple Choice

What is the principal root of √25?

• 2

• 5

• 10

• 100

Multiple Choice

What is the principal root of √10?

• 3.162277660…

• 5

• 10

• 100

Multiple Choice

Which of the following describes the principal root of √50?

• Integers

• Integers

• Integers

• Integers

Multiple Choice

Which of the numbers is classified as perfect square integer?

• 6

• 9

• 12

• 20

Multiple Choice

Between what two consecutive integers does the square root of 18 lie?

• 3 & 4

• 4 & 5

• 5 & 6

• 16 & 25

Multiple Choice

Find the number whose square root lies between 5 and 6.

• 24

• 25

• 26

• 36

Multiple Choice

Find the square root of 16.

• 4

• 5

• 6

• 8

Multiple Choice

Which of the following has an irrational principal root?

• 4

• 9

• 16

• 20

Multiple Choice

Which of the following square roots lies between 2 and 3.

• √2

• √3

• √5

• √10

Multiple Choice

Which of the following is not a perfect square integer?

• 25

• 49

• 63

• 81

Multiple Choice

Between what two consecutive integers does the square root of 33 lie?

• 4 & 5

• 5 & 6

• 6 & 7

• 7 & 8

Multiple Choice

Find the principal root of √121 .

• 10

• 11

• 12

• 13

​NOTE

• You may use the scientific calculator in your android phone to easily check the principal root of a number.

Fill in the Blank

Find the product of the following:

1x1

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Find the product of the following:

2x2

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Find the product of the following:

3x3

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Find the product of the following:

4x4

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Find the product of the following:

5x5

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Find the product of the following:

6x6

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Find the product of the following:

7x7

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Find the product of the following:

8x8

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Find the product of the following:

9x9

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Find the product of the following:

10x10

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Tell whether the given number is Rational or Irrational:

25

Fill in the Blank

Tell whether the given number is Rational or Irrational:

$$\frac{1}{2}$$  

Fill in the Blank

Tell whether the given number is Rational or Irrational:

$$\sqrt[]{3}$$  

Fill in the Blank

Tell whether the given number is Rational or Irrational:

1.414235…

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Tell whether the given number is Rational or Irrational:

3.666...

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Determine whether the Principal Root of a number is Rational or Irrational:

√49

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Determine whether the Principal Root of a number is Rational or Irrational:

√3

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Determine whether the Principal Root of a number is Rational or Irrational:

√50

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Determine whether the Principal Root of a number is Rational or Irrational:

√26

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Determine whether the Principal Root of a number is Rational or Irrational:

√81

Multiple Choice

Determine between what two consecutive integers each principal root lie:

√77

• 8 and 9

• 7and 8

• 9 and 10

• 6 and 7

Multiple Choice

Determine between what two consecutive integers each principal root lie:

√87

• 8 and 9

• 7and 8

• 9 and 10

• 6 and 7

Multiple Choice

Determine between what two consecutive integers each principal root lie:

√50

• 8 and 9

• 7and 8

• 9 and 10

• 6 and 7

Multiple Choice

Determine between what two consecutive integers each principal root lie:

√136

• 8 and 9

• 7and 8

• 11 and 12

• 6 and 7

Multiple Choice

Determine between what two consecutive integers each principal root lie:

√243

• 8 and 9

• 15 and 16

• 11 and 12

• 6 and 7

Fill in the Blank

Which country consumes the most chocolate per head?

To answer that question, determine between what particular range of integers the square root of each number lie and write the letter in the box that corresponds to your answer.

Refer to the image in the left.

Multiple Choice

What do you call a number that can be expressed in the form  $$\frac{a}{b}$$  , where a and 𝑏 b are integers, and b is not equal to 0?

• Integers

• Irrational

• natural

• rational

Multiple Choice

What do you call the positive n^th root of a number?

• perfect square

• principal root

• radical

• radicand

Multiple Choice

Which of the following refers to a number whose decimal representation is neither terminating nor repeating? This number cannot be expressed as a quotient of integers.

• Integers

• Irrational

• natural

• rational

Multiple Select

What is the principal root of √81?

• -9

• 8

• 9

• 81

Multiple Choice

What is the principal root of $$\frac{\sqrt[]{9}}{\sqrt[]{4}}$$  ?

• $$\frac{3}{2}$$  

• $$\frac{3}{4}$$  

• $$\frac{9}{2}$$  

• $$\frac{9}{4}$$  

Multiple Choice

Which of the following best describes the principal root of √50?

• integer

• irrational

• natural

• rational

Multiple Choice

Which of the following best describes the principal root of √121?

• integer

• irrational

• natural

• rational

Multiple Choice

Which of the statements is TRUE?

• √7 is an integer

• √16 is an irrational numberal

• √25 is a rational number

• √90 is neither rational nor irrational number

Multiple Choice

Find the number whose square root lies between 8 and 9?

• 8

• 9

• 75

• 85

Multiple Choice

Between what two consecutive integers does the square root of 118 lie?

• 8 & 9

• 9 & 10

• 10 & 11

• 11 & 12