Worksheet on Completing Square

Practice the questions given in the worksheet on completing square.

1. Write the following as a perfect square.

(i) 4X$^{2}$ + 4X + 1

(ii) 9a$^{2}$ – 12ab + 4b$^{2}$

(iii) 1 + $\frac{6}{a}$ + $\frac{9}{a^{2}}$

2. Indicate the perfect squares among the following. Express each of the perfect squares as the square of a binomial. What numbers should be added to those which are not perfect squares so that the expressions may become perfect squares?

(i) 36x$^{2}$ – 60xy + 25y$^{2}$

(ii) x$^{2}$ + 4x + 1

(iii) 4a$^{2}$ + 4a

(iv) 9a$^{2}$ – 6a + 1

(v) 16 – 24a + 9a$^{2}$

(vi) 25x$^{2}$ + 10x – 1

3. Find the missing term in each of the following so that the expression becomes a perfect square.

(i) 25x$^{2}$ + (..........) + 49

(ii) 64a$^{2}$ - (..........) + b$^{2}$

(iii) 9 + (..........) + x$^{2}$

(iv) 16a$^{2}$ + 8a + (..........)

(v) (..........) – 18x + 9x$^{2}$

(vi) x$^{2}$ – 2 + (..........)

4. Each of the following is a perfect square. Find the numerical value of k.

(i) 121a$^{2}$ + ka + 1

(ii) 3ka$^{2}$ + 24a + 4

[Hint: 3ka$^{2}$ + 2 ∙ 6a ∙ 2 + 2$^{2}$. So, 3ka$^{2}$ = (6a)$^{2}$. Therefore, 3k = 6$^{2}$]

(iii) 4x$^{4}$ + 12x$^{2}$ + k

5. What should be added to make each of the following a perfect square?

(i) 25x$^{2}$ + 81

(ii) 81x$^{2}$ – 18x

(iii) a$^{4}$+ $\frac{1}{a^{4}}$

Answers for the worksheet on completing square are given below.

Answer:

1. (i) (2x + 1)$^{2}$

(ii) (3a – 2b)$^{2}$

(iii) (1 + $\frac{3}{a}$)$^{2}$

2. (i) Perfect square, (6x – 5y)$^{2}$

(ii) Not a perfect square, 3

(iii) Not a perfect square, 1

(iv) Perfect square, (3a - 1)$^{2}$

(v) Perfect square, (4 – 3a)$^{2}$

(vi) Not a perfect square, 2

3. (i) 70x

(ii) 16ab

(iii) 6x

(iv) 1

(v) 9

(vi) $\frac{1}{x^{2}}$

4. (i) 22

(ii) 12

(iii) 9

5. (i) 90x

(ii) 1

(iii) 2 or -2

9th Grade Math

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