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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