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Q.9  There are 500 children in a school. For a P.T. drill they have to stand in such a manner that the number of rows is equal to number of columns. How many children would be left out in this arrangement.

Given that the number of rows is equal to the number of columns.    i.e., in the form of    So the number of students that can stand in this order will be the perfect square number just less than 500. We know that                    and       So the number of students that would be left out in this arrangement = 500 - 484 = 16 students.

Q.8  A gardener has 1000 plants. He wants to plant these in such a way that the number of rows and the number of columns remain same. Find the minimum number of plants he needs more for this.

It is given that the number of rows and the number of columns are the same. Let a number of rows or number of columns be x. The number of plants required  =   The gardener has 1000 plants. We need to find a perfect square just greater than 1000. We know,                      and          So the minimum plants needed by gardener = 1024 - 1000 = 24 plants.

Q.7 In a right triangle ABC,\angle B=90^{\circ}

(b)  If AC=13\; cm, BC=5\; cm, find AB

Using Pythagoras theorem,                       or                  or                 or                  Prime factorisation of 144 gives :-   Hence,                        AB = 12 cm

7. In a right triangle ABC, \angle B=90^{\circ}

(a)  If AB=6cm, BC=8cm, find AC

Using Pythagoras theorem,                     By prime factorisation of 100 :-    We get,                                   AC = 10cm 

Q.6  Find the length of the side of a square whose area is 441\; m^{2}.

Let the length of the side of a square be x m. Area of square =  So equation becomes :       By prime factorisation of 441. 441 =  Thus x = 21. So the length of the side of square = 21 m.

Q.5 Find the least number which must be added to each of the following numbers 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

(i) 525:-    It is clearly visible that if we add 4 to the given number, the remainder will become zero.                   So obtained number is 529 and its square root is 23.(ii) 1750:-    It is clearly visible that if we add 14 to the given number, the remainder will become zero.                   So the obtained number is 1764 and its square root is 42. (iii) 252:-  It is clearly visible...

4.Find the least number which must be subtracted from each of the following numbers 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

 

(i)    402 :-     It can be seen that 2 is remainder. So we will subtract 2 from 402.                        The required number is 400 and its square root is 20.                    (ii) 1989 :-       It can be seen that 53 is remainder here. So we will subtract 53 from 1989 in order to make it a perfect square.                        The required number is 1936 and its square root is 44. ...

Q.3. Find the square root of the following decimal numbers.

(i) 2.56

(ii) 7.29

(iii) 51.84

(iv) 42.25

(v) 31.36

   The detailed solution for the given questions as follows (i) Square root of 2.56 using division method (ii)  Square root of 7.29 using division method                                          (iii) Square root of 51.84 using division method                                                   (iv)  Square root of 42.25 using division method                                                     ...

Q.2 Find the number of digits in the square root of each of the following numbers (without any calculation).

(i) 64

(ii) 144

(iii) 4489

(iv) 27225

(v) 390625

(i) 64:-     The number of digits in the square root will be                                      (ii) 144:-   The number of digits in the square root will be                                     (iii) 4489:- The number of digits in the square root will be                                 (iv) 27225:-  The number of digits in the square root will be                             (v) 390625:-   The...

Q.1 Find the square root of each of the following numbers by Division method.

(xii) 900

The detailed solution for the above-written question is as follows The square root of 900 is 30.

Q.1 Find the square root of each of the following numbers by Division method.

(xi) 3136

The detailed solution for the above-written question is as follows, The square root of 3136 is 56.

Q1. Find the square root of each of the following numbers by Division method.

(x) 1024

The detailed solution for the above-written question is as follows, The square root of 1024 is 32.

Q1.Find the square root of each of the following numbers by Division method.

(ix) 576

The detailed solution for the above-written question is as follows, The square root of 576 is 24.

Q1.Find the square root of each of the following numbers by Division method.

(viii) 7921

The detailed solution for the above-written question is as follows, The square root of 7921 is 89.

Q1. Find the square root of each of the following numbers by Division method.

(vii) 5776

The solution for the above-written question is as follows, The square root of 5776 is 76.

Q1. Find the square root of each of the following numbers by Division method.

(vi) 1369

The detailed solution for the above-written question is as follows, The square root of 1369 is 37.

Q1.Find the square root of each of the following numbers by Division method.

(v) 3249

The detailed solution for the above-written question is as follows, The square root of 3249 is 57.

Q1. Find the square root of each of the following numbers by Division method.

(iv) 529

The detailed solution for the above-written question is as follows The square root of 529 is 23.

Q.1 Find the square root of each of the following numbers by Division method.

(iii) 3481

The detailed solution for the above-written question is as follows, The square root of 3481 is obtained as 59.

Q.1 Find the square root of each of the following numbers by Division method.

(ii) 4489

The detailed solution for the above-written question is as follows The square root of 4489 is 67.
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