Squares and Square Roots - Worksheets

CBSE Worksheet-1
Class 08 - Mathematics (Square and square roots)

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General Instructions: All questions are compulsory. Q.1 to Q.2 carries one mark each. Q.3 to Q.7 carries two marks each. Q.8 and Q.9 carries three marks each. Q.10 to Q.12 carries four marks each.

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1. What will be the unit digit of the square of 55555 ?
2. Without calculating square roots, find the number of digits in the square root of 36864.
3. State true or false:
   1. 24 numbers lie between squares of the number 12 and 13.
   2. The value of √1.030225 is 1.015
   3. The smallest number by which 32 should be multiplied so as to get perfect square is 2.
   4. If 102 = 100, then the square root of 100 is 1000.
4. Fill up the following:
   1. 49 as the sum of odd number is ______.
   2. The square root of 1.21 is ______.
   3. The square root of 20 lies the pair of whole numbers between ______.
   4. The square root of 196 is ______.
5. Match the following:

   Column A	Column B
   1. √1.69	(a) 8.7
   2. √33.64	(b) 12.5
   3. √156.25	(c) 5.8
   4. √75.69	(d) 1.3

6. The following numbers are obviously not perfect squares. Give reason.
   (i) 222000
   (ii) 505050
7. Is 1069 perfect square ? How do we know ?
8. Find the least number which must be added to 252 so as to get a perfect square. Also find the square root of the perfect square so obtained.
9. Find the least number which must be subtracted from 402 so as to get a perfect square. Also find the square root of the perfect square so obtained.
10. By what number should 14700 be divided to get a perfect square? Also find the square root of the perfect square obtained.
11. Simply the following:
    125−−−√×320−−−√$\sqrt{125}\times \sqrt{320}$
12. Find the smallest whole number with which 252 should be divided so as to get a perfect square. Also find the square root of the square number so obtained.

CBSE Worksheet-1
Class 08 - Mathematics (Square and square roots)
Solution

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1. The unit digit of the square of the number 55555 will be 5.
2. 36864
   By placing bars, we get 3¯¯¯68¯¯¯¯¯64¯¯¯¯¯$\overline{3}\overline{68}\overline{64}$
   Since there are 3 bars, the square root will be of 3 digits.
3. 1. True
   2. True
   3. True
   4. False
4. 1. 1 + 3 + 5 + 7 + 9 + 11 + 13
   2. 1.1
   3. 4 and 5
   4. 14
5. 1. (d)
   2. (c)
   3. (b)
   4. (a)
6. (i) 222000. The number 222000 is not a square number because the number of zeroes at end of a square number ending with zeros is always even.
   (ii) 505050. The number 505050 is not a square number because the number of zeroes at the end of a square number ending with zeros is always even.
7. The number 1069 ends in 9. But we cannot say that 1069 is a perfect square number.
   3432, 2453, 5447, 6758, 4562
8. 
   This shows that 152 < 252
   Next perfect square is 162 = 256
   Hence, the number to be added is 162 – 252 = 256 – 252 = 4
   Therefore, the perfect square so obtained is 252 + 4 = 256
   Hence, 256−−−√$\sqrt{256}$ = 16.
9. 
   This shows that 202 is less than 402 by 2. This means, if we subtract the remainder from the number, we get a perfect square, So, the required least number is 2.
   Therefore, the required perfect square is 402 – 2 = 400.
   Hence, 400−−−√=20$\sqrt{400}=20$.
10. 14700 = 5× 5 × 2 × 2 × 7 × 7 × 3
    = (5× 5) × (2 × 2) × (7 × 7) × 3
    Since the factor 3 is not in pair.
    ∴ The given number should be divide by 3.
    14700 ÷ 3 = 4900
    √4900 = 70
11. 125−−−√×320−−−√=125×320−−−−−−−−√$\sqrt{125}\times \sqrt{320}=\sqrt{125\times 320}$
    =5×25×5×64−−−−−−−−−−−−√$=\sqrt{5\times 25\times 5\times 64}$
    =5×5×5×5×8×8−−−−−−−−−−−−−−−−√$=\sqrt{5\times 5\times 5\times 5\times 8\times 8}$
    =5×5×8$=5\times 5\times 8$
    =25×8=200$=25\times 8=200$
12. The prime factorisation of 252 is 252 = 2 × 2 × 3 × 3 × 7
    We see that prime factor 7 has no pair. So, if we divide 252 by 7, then we get
    
    252 ÷ 7 = 2 × 2 × 3 × 3
    Now each prime factor has a pair. Therefore, 252 ÷ 7 = 36 is a perfect square. Thus, the required smallest number is 7.
    Hence, 36−−√$\sqrt{36}$ = 2 × 3 = 6.