Question

SQUARES AND SQUARE ROOTS 1. Find the square root of 6400 2. Is 90 a perfect square 3. Is 2352 a perfect square? If not find the smallest multiple of2352 which is a perfect square. Find the square root of the new number. 4. Find the smallest number by which 9408 must be divided so that the quotient is a perfect square. Find the square root of the quotient. 5. Without doing any calculation, find the numbers which are surely not perfect square. i.) 153 ii.) 257 iii) 408 iv.) 441 6. Find the square root of the following numbers by the prime factorisation method. i.) 400 ii.) 9604 iii.) 8100 iv.)1764 v.) 5929 vi.) 9216 7. For each of the following numbers, find the smallest whole number by which it should be multiplied so as to get a perfect square. also find the square root of the square number so obtained. i.) 252 ii.) 2925 iii.) 396 iv.) 2028 v.) 1458 vi.) 768 8. For each of the following number, find the smallest whole number by which it should be divided so as to get a perfect square. Also find the square root of the square number so obtained. i.) 252 ii.) 180 iii.) 1008 iv.) 2028 v.) 1458 vi.) 768 9. The students of class viii of a school donated Rs 2401 in all, for prime minister’s national relief fund. each student donated as many rupees as the no: of students in the class. Find the no: of students in the class. 10.2118 plants are to be planted in a garden in such a way that each row contains as many plants as the no: of rows. Find the no: of rows and the no: of plants in each row. 11.Find the smallest square no: that is divisible by each of the no: 4, 9and10. 12.Find the smallest square no: that is divisible by each of the no: 8, 15 and 20. 13.Find the least no: that must be subtracted from 5607 so as to get a perfect square. Also find the square root of the perfect square. 14.Find the greatest 4- digit no: which is a perfect square. 15.Find the least no: that must be added to 1300 so as to get a perfect square .Also finds the square root of the perfect square. 16.Find the square root of 12.25. 17.Area of a square plot is 2304m2 . find the side of the square plot. also find the square root of the perfect square. 18.find the square root of each of the following no: by division method. i.) 2304 ii.) 4489 iii.) 3481 iv.) 529 v.) 3249 vi.) 1369 vii.) 5776 viii.)7921 ix.) 576 x.) 1024 xi.) 3136 xii.) 900 19.Find the square root of the following decimal no: 2.56 ii 7.29 iii. 51.84 iv 42.25 v 31.36 20.Find at least no: which must be subtracted from each of the following no:so as to get a perfect square. Also find the square root of the perfect square so obtained. i. 402 ii.1989 iii. 3250 iv. 825 v. 4000 21.Find the least no: which must be added to each of the following no: so as to get a perfect square. Also find the square root of the perfect square so obtained. i. 525 ii. 1750 iii. 252 iv. 1825 v. 6412 22.Find the length of the side of a square whose area is 441m2. 23. In a right triangle ABC angle B = 90o 24.a. If AB=6 cm, BC=8cm, find AC b. If AC=13cm,BC= 5cm, find AB 25.A gardener has 1000 plants. He wants to plant this in such a way that the no: of rows and the no: of columns remain same. Find the minimum no: of plants he needs more for this.26.There are 500 children in a school. for a P.Ed. drill. They have to stand in such a manner that the no. of rows is equal to the no: of columns. How many children would be left out in this arrangement? [least no :] Worksheet 1. A natural number is called a ____________ or ___________ if it is the square of some natural number. 2. √ 0.09 = _________ . 3. 1 x √ 5.76 = ________ . √ 0.09 4. 1212 - 1202 = ___________ . 5. Is ( 1, 2, 3 ) a Pythagorean triplet ? 6. Is 2352 a perfect square? If not, find the smallest number by which 2352 must be multiplied so that the product is a perfect square. Find the square root of the perfect square obtained. 7. Find the smallest number by which 9408 must be divided so that the quotient is a perfect square. Find the square root of the perfect square obtained. 8. The student of class VIII of a school donated Rs.2401 for prime ministers National relief fund. Each student donated as many rupees as the number of students in the class. Find the number of students in the class. 9. Find the least number which must be subtracted from 18265 so as to get a perfect square. 10. Find the least number which must be added to 893304 to obtain a perfect square. 11. Find the square root of 2.9 correct to two places of decimal. 12. Find the square root of 11 2 /3 correct to two places of decimal. 13. Find the square root of 21 51 . 169 14. Find the least perfect square which is divisible by 5 , 6 and 8. 15. Find the smallest five digit number which is a perfect square. 16. Find the other two members of a Pythagorean triplet, one of the number of which is 16. 17. Check, is ( 12 , 35, 37 ) a Pythagorean triplet?

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