# 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.

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

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