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Mathematics Notes for 9th Class Exercise 6.3

“Math” a compulsory subject for 9th class Science students. and Mathematics Notes for 9th Class Exercise 6.3 or Math Notes Class 9 English Medium (Science Group) included in this book.

How to Find Square Root of Algebraic Expression:

As with numbers define the square root of given expression p(x) as another expression q(x) such that q(x) . q(x) = p(x). As 5 # 5 = 25, so square root of 25 is 5.  It means we can find square root of the expression p(x) if it can be expressed as a perfect square.
In this section we shall find square root of an algebraic expression
(i) Square Root by factorization (ii) Square Root by division

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Math Ch#6, 09th Class

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1 / 17

H. C. F of  ( p^{3}q-pq^{3} ) and ( p^{5}q^{2}-p^{2}q^{5} ) is ___________

  • pq(p^{2}-q^{2})
  • pq(p-q)
  • p^{2}q^{2} (p-q)
  • pq(p^{3}-q^{3})

(Select Correct Option)

2 / 17

Simplify \frac{a^2 +5a-14}{a^2 - 3a-18} \times \frac{a+3}{a-2} = _________

  • \frac{a+7}{a-6}
  • \frac{a+7}{a-2}
  • \frac{a+3}{a-6}
  • \frac{a-2}{a+3}

(Choose Correct Option)

3 / 17

H.C.F of x-2 and x^{2}+x-6 is ___________

  1. x^{2}+x-6
  2. x+3
  3. x-2
  4. x+2

(Chose Correct Option)

4 / 17

Simplify \frac{a^3-b^3}{a^4-b^4} \div \frac{a^2+ab+b^2}{a^2+b^2} = ________

  • \frac{1}{a+b}
  • \frac{1}{a-b}
  • \frac{a-b}{a^2+b^2}
  • \frac{a+b}{a^2+b^2}

(Which option is Correct)

5 / 17

L.C.M of a^2+b^2 and a^4 - b^4 is _________

  1. a^2+b^2
  2. a^2-b^2
  3. a^4-b^4
  4. a-b

(Choose Correct Option)

6 / 17

H.C.F of 5x^{2} and 20 x^{3} y^{3} is ____________

  • 5x^{2}y^{2}
  • 20x^{3}y^{3}
  • 100x^{5}y^{5}
  • 5xy

(Select Correct Option)

7 / 17

The Square Root of x^4 + \frac{1}{x^4}+2 is ___________

  • \pm \left ( x + \frac{1}{x} \right )
  • \pm \left ( x^2 + \frac{1}{x^2} \right )
  • \pm \left ( x - \frac{1}{x} \right )
  • \pm \left ( x^2 - \frac{1}{x^2} \right )

Select Correct Option

8 / 17

The product of two Algebraic expressions is equal to the ______ of their H.C.F and L.C.M

9 / 17

H.C.F of a^{3}+b^{3} and a^{2}-ab+b^{2} is ________

  1. a+b
  2. a^{2}-ab+b^{2}
  3. (a-b)^2
  4. a^2+b^2

(Chose Correct Option)

10 / 17

H.C.F of x^2 +3x+2 , x^2+4x+3 and x^2+5x+4 is __________

11 / 17

Simplify \left ( \frac{2x+1}{x+y}-1 \right )\div \left ( 1-\frac{x}{x-y} \right ) = __________

  • \frac{x}{x+y}
  • \frac{y}{x+y}
  • \frac{y}{x}
  • \frac{x}{y}

Which Option is Correct

12 / 17

L.C.M of 15x^2 , 45xy , 30xyz is __________

  1. 90xyz
  2. 90x^2yz
  3. 15xyz
  4. 15x^2yz

(Choose Correct Option)

13 / 17

the Square Root of a^2 - 2a + 1 is __________

14 / 17

What should be added to complete the square of x^4 + 64 _____

  • 8x^2
  • -8x^2
  • 16x^2
  • 4x^2

Select Correct Option

15 / 17

H.C.F of x^2 - 5x+6 and x^2 - x-6 is _______

16 / 17

Simplify \frac{a}{9a^2 - b^2} + \frac{1}{3a-b} = __________

  1. \frac{4a}{9a^2-b^2}
  2. \frac{4a-b}{9a^2-b^2}
  3. \frac{4a+b}{9a^2-b^2}
  4. \frac{b}{9a^2-b^2}

(Choose Correct Option)

17 / 17

H.C.F of a^2 - b^2  and a^3 - b^3  is ________

  1. a -b
  2. a+b
  3. a^2 + ab+ b^2
  4. a^2 - ab+b^2

(Choose Correct Option)

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Math Solution 9th Class (Science Group)

Exercise 1.1           (English)            (Urdu)


Exercise 1.2           (English)            (Urdu)


Exercise 1.3           (English)            (Urdu)


Exercise 1.4           (English)            (Urdu)


Exercise 1.5           (English)            (Urdu)


Exercise 1.6           (English)            (Urdu)


Exercise 1-Rev      (English)            (Urdu)


Online Practice/ Test - MCQs & Short Questions

Exercise 2.1           (English)            (Urdu)


Exercise 2.2           (English)            (Urdu)


Exercise 2.3           (English)            (Urdu)


Exercise 2.4           (English)            (Urdu)


Exercise 2.5           (English)            (Urdu)


Exercise 2.6           (English)            (Urdu)


Exercise 2-Rev      (English)            (Urdu)


Online Practice/ Test - MCQs & Short Questions

Exercise 3.1           (English)            (Urdu)


Exercise 3.2           (English)            (Urdu)


Exercise 3.3           (English)            (Urdu)


Exercise 3.4           (English)            (Urdu)


Exercise 3-Rev      (English)            (Urdu)


Online Practice/ Test - MCQs & Short Questions

Exercise 4.1           (English)            (Urdu)


Exercise 4.2           (English)            (Urdu)


Exercise 4.3           (English)            (Urdu)


Exercise 4.4           (English)            (Urdu)


Exercise 4-Rev      (English)            (Urdu)


Online Practice/ Test - MCQs & Short Questions

Exercise 5.1           (English)            (Urdu)


Exercise 5.2           (English)            (Urdu)


Exercise 5.3           (English)            (Urdu)


Exercise 5.4           (English)            (Urdu)


Exercise 5-Rev      (English)            (Urdu)


Online Practice/ Test - MCQs & Short Questions

Exercise 6.1           (English)            (Urdu)


Exercise 6.2           (English)            (Urdu)


Exercise 6.3           (English)            (Urdu)


Exercise 6-Rev      (English)            (Urdu)


Online Practice/ Test - MCQs & Short Questions

Exercise 7.1           (English)            (Urdu)


Exercise 7.2           (English)            (Urdu)


Exercise 7.3           (English)            (Urdu)


Exercise 7-Rev      (English)            (Urdu)


Online Practice/ Test - MCQs & Short Questions

Exercise 8.1           (English)            (Urdu)


Exercise 8.2           (English)            (Urdu)


Exercise 8.3           (English)            (Urdu)


Exercise 8-Rev      (English)            (Urdu)


Online Practice/ Test - MCQs & Short Questions

Exercise 9.1           (English)            (Urdu)


Exercise 9.2           (English)            (Urdu)


Exercise 9.3           (English)            (Urdu)


Exercise 9-Rev      (English)            (Urdu)


Online Practice/ Test - MCQs & Short Questions

Exercise 10.1           (English)            (Urdu)


Exercise 10.2           (English)            (Urdu)


Exercise 10.3           (English)            (Urdu)


Exercise 10.4           (English)            (Urdu)


Exercise 10-Rev      (English)            (Urdu)


Online Practice/ Test - MCQs & Short Questions

Exercise 11.1           (English)            (Urdu)


Exercise 11.2           (English)            (Urdu)


Exercise 11.3           (English)            (Urdu)


Exercise 11.4           (English)            (Urdu)


Exercise 11.5           (English)            (Urdu)


Exercise 11-Rev      (English)            (Urdu)


Online Practice/ Test - MCQs & Short Questions

Exercise 12.1           (English)            (Urdu)


Exercise 12.2           (English)            (Urdu)


Exercise 12.3           (English)            (Urdu)


Exercise 12-Rev      (English)            (Urdu)


Online Practice/ Test - MCQs & Short Questions

Exercise 13.1           (English)            (Urdu)


Exercise 13.2           (English)            (Urdu)


Exercise 13-Rev      (English)            (Urdu)


Online Practice/ Test - MCQs & Short Questions

Exercise 14.1           (English)            (Urdu)


Exercise 14.2           (English)            (Urdu)


Exercise 14-Rev      (English)            (Urdu)


Online Practice/ Test - MCQs & Short Questions

Exercise 15           (English)            (Urdu)


Exercise 15-Rev   (English)            (Urdu)


Online Practice/ Test - MCQs & Short Questions

Exercise 16.1           (English)            (Urdu)


Exercise 16.2           (English)            (Urdu)


Exercise 16-Rev      (English)            (Urdu)


Online Practice/ Test - MCQs & Short Questions

Exercise 17.1           (English)            (Urdu)


Exercise 17.2           (English)            (Urdu)


Exercise 17.3           (English)            (Urdu)


Exercise 17.4           (English)            (Urdu)


Exercise 17.5           (English)            (Urdu)


Exercise 17-Rev      (English)            (Urdu)


Online Practice/ Test - MCQs & Short Questions


9th Math Science Group (English Medium)


9th Math Science Group (Urdu Medium)


9th Math Arts Group (Urdu Medium)



Mathematics Notes for 9th Chapter # 06:

(i) By Factorization:

First we seen how find the square root by factorization.

(ii) By Division:

we have also seen the division method, when it is difficult to convert the given expression into a perfect square by factorization, we use the method of actual division to find its square root. The method is similar to the division method of finding square root of numbers.

There are Seventeen chapters in Mathematics 9th Class for Punjab Textbook Board, Lahore. Solutions of all the chapters are given below. Anyone can download the PDF file of the notes. Note that, you can view these notes only if you have PDF reader software/ App on your device. However online view of the notes is also available on eStudent.pk . You can find all solution along with 9th Class Math Notes in Urdu (Science Group), Math MCQs Class 9. 

Math Notes Class 9:

9th class math notes chapter 6, 9th class math solution chapter 6 pdf, math notes class 9 chapter 6, Math Notes Class 9 Exercise 6.3, exercise 6.3 class 9, exercise 6.3 class 9 then this post is specially for you and your future. All Boards of Intermediate & Secondary Educations in Punjab, Federal Board of Intermediate and Secondary Education, kpd board, Sindh board, Agha Khan Board and also Allama Iqbal Open University are taking examination according to Mathematics 9th Class. 9th Class Math key book pdf in English, Notes of 9th Class Math, Mathematics Notes for 9th Class Exercise 6.3.

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