First Quarter
MATHEMATICS 7
Learning Module No. 6
Name: _________________________________ Date: ___________________
Grade level & Section__________________ Score: __________________
Name of Subject Teacher: Reyboy P. Tagsip
Topic: Principal Roots and Irrational Numbers (Page 191-199)
Duration: Week 6-September 20-24, 2021
Learning Competencies:
1. describes principal roots and tells whether they are rational or irrational
2. determines between what two integers the square root of a number is
3. estimates the square root of a whole number to the nearest hundredth
4. plots irrational numbers (up to square roots) on a number line.
Learning Objectives: Students were expected to:
1. describe and define irrational numbers;
2. describe principal roots and tell whether they are rational or irrational;
3. determine between what two integers the square root of a number is;
4. estimate the square root of a number to the nearest tenth;
5. illustrate and graph irrational numbers (square roots) on a number line with and without appropriate technology.
References: My Distance Learning Buddy a Modular Textbook for the 21 st Century Learner, Alen L. Tuliao., et.al.2020,
Mathematics Learner’s Material, DepEd 2013, Elizabeth R. Aseron, et.al
INTRODUCTION
In this lesson, you will learn about irrational numbers and principal nth roots, particularly square roots of numbers.
You learned to find two consecutive integers between which an irrational square root lies. You’ll also learn how to
estimate the square roots of numbers to the nearest tenth and how to plot the estimated square roots on a number line.
PRE-TEST
A. Take a look at the unusual wristwatch and answer the questions
below.
1. Can you tell the time?
2. What time is shown in the wristwatch?
3. What do you get when you take the √ 1 ? √ 4 ? √ 9 ? √ 16 ?
CONTENT
Important Terms to Remember
The following are terms that you must remember from this point on.
Taking the square root of a number is like doing the reverse operation of squaring a number. For
example, both 7 and -7 are square roots of 49 since 72 49 and (−7)2 49 . Integers such as 1, 4, 9, 16, 25
4
and 36 are called perfect squares. Rational numbers such as 0.16, and 4.84 are also, perfect squares.
100
Perfect squares are numbers that have rational numbers as square roots. The square roots of perfect squares
are rational numbers while the square roots of numbers that are not perfect squares are irrational numbers.
Any number that cannot be expressed as a quotient of two integers is an irrational number. The
numbers √ 2 , , and the special number e are all irrational numbers. Decimal numbers that are non-repeating
and non-terminating are irrational numbers.
You may visit this link for further explanation. https://www.youtube.com/watch?v=mFVCWcR7H-4
Please read the content of the topic stated on your book on page 191-199. If you have some clarifications or clear process
of examples, kindly message me in the group chat so that all of your classmates will see.
Enrichment Activity
Answer the Let’s Practice found on your book. Read carefully the instructions and write you answers on the
space provided.
Let's Practice
A. Determine if each expression is rational, irrational, or not real. You can use your scientific calculator to easily know
the results if it is rational, irrational, or not real.
1. √ 1 ______________ 2. -√ 25 ______________
3. √ 15 ______________ 4. √ 400 ______________
5. √ −36 _____________
B. Determine whether each statement is true or false.
_______ 1. √ 4=± 2
_______ 2. 169 is a perfect square.
_______ 3. In the expression √ 25, 25 is the root.
_______ 4. ± √−9=−3
_______ 5. √ 11 is irrational.
C. Each irrational number lies between two consecutive integers. Determine these consecutive integers for each item
below.
Example. √ 35=5.91 So, √ 35 lies between 5 or may classified as √ 25 and 6 as √ 36.
√ 25< √ 35< √ 36
5 ¿ √ 35 ¿ 6
1. √ 7 ___ , ___ 2. √ 85 ___ , ___
3. √ 29 ___ , ___
D. Plot the following on a number line. Also, write the two consecutive numbers where the plotted value being in
between. See Example 3 to know how to plot. Page 197.
1. √ 0 2. √ 121
3. − √ 49
E. Evaluate the following (Ex. ± √36 = ± 6)
1. √ 144 = ____ 2. −√ 49 = ____
3. −√ 121 = ____
F. Without Using calculator, estimate the following to the nearest tenth. (Ex. √ 18 = 4.2)
1. √ 5 = ____ 2. √ 16 = ____
3. √ 77 = ____
G. Use a calculator to determine the approximate value of the number up to two decimal places.
1. √ 14 = ____ 2. −√ 8 = ____
3. −√ 15 = ____
H. Use a calculator to determine the approximate value of the number up to five decimal places. (Ex. √ 23 = 4.79583)
1. ± √ 20 = _________ 2. √ 11 = _________
1
3. −2 √ 2 = _________ 4. √ 5 = _________
2
5. π = _________
Prepared by: Checked by:
REYBOY P. TAGSIP REYBOY P. TAGSIP
Subject Teacher Mathematics Subject Area Coordinator
Noted by:
MIRA ROCHENIE C. PIQUERO
Academic Coordinator
Approved by:
MA. NANETTE D. BAYONAS
School OIC-Principal
ANSWER KEY
Let's Practice
A. Determine if each expression is rational, irrational, or not real. You can use your scientific calculator to easily know
the results if it is rational, irrational, or not real.
1. √ 1 ______Rational________ 2. -√ 25 ______rational________
3. √ 15 ______Irrational________ 4. √ 400 ______rational________
5. √ −36 _________not real____
B. Determine whether each statement is true or false.
___t____ 1. √ 4=± 2
___t____ 2. 169 is a perfect square.
___f____ 3. In the expression √ 25, 25 is the root.
___f____ 4. ± √−9=−3
___t____ 5. √ 11 is irrational.
C. Each irrational number lies between two consecutive integers. Determine these consecutive integers for each item
below.
Example. √ 35=5.91 So, √ 35 lies between 5 or may classified as √ 25 and 6 as √ 36.
√ 25< √ 35< √ 36
5 ¿ √ 35 ¿ 6
1. √ 7 _2__ , _3__ 2. √ 85 _9__ , _10__
3. √ 29 _5__ , _6__
D. Plot the following on a number line. Also, write the two consecutive numbers where the plotted value being in
between. See Example 3 to know how to plot. Page 197.
1. √ 0 2. √ 121
3. − √ 49
E. Evaluate the following (Ex. ± √36 = ± 6)
1. √ 144 = __12__ 2. −√ 49 = _-7___
3. −√ 121 = ___-11_
F. Without Using calculator, estimate the following to the nearest tenth. (Ex. √ 18 = 4.2)
1. √ 5 = _2.2___ 2. √ 16 = __4.0__
3. √ 77 = __8.8__
G. Use a calculator to determine the approximate value of the number up to two decimal places.
1. √ 14 = __3.74__ 2. −√ 8 = _-2.83___
3. −√ 15 = __-3.87__
H. Use a calculator to determine the approximate value of the number up to five decimal places. (Ex. √ 23 = 4.79583)
1. ± √ 20 = ____± 4.47214 _____ 2. √ 11 = __3.31662_______
1
3. −2 √ 2 = ___-2.82843______ 4. √ 5 = ___1.11803______
2
5. π = ___3.14159______
