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
From Worksheet on Completing Square to HOME PAGE
Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.
Apr 13, 24 05:12 PM
Apr 13, 24 03:29 PM
Apr 13, 24 01:27 PM
Apr 13, 24 12:41 PM
Apr 12, 24 04:22 PM
New! Comments
Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.