Place the given numbers in the respective columns. 20 , 27 , 50 , 75 , 100 , 108 , 144 , 169 , 180 , 256 Square number Not square number What is the least positive integer which when multiplied by the given number gives a square number

The given numbers are to be placed in the below table. 20 , 27 , 50 , 75 , 100 , 108 , 144 , 169 , 180 , 256 Square number Not square number What is the least positive integer which when multiplied by the given number gives a square number A perfect square number, from a given number system, that can be expressed as the square of a number from the same number system. Also, a non-perfect square number is a number that is not the result of squaring an integer with itself. From the above given definition. Perfect squares- 100 = 10 × 10 ; 144 = 12 × 12 ; 169 = 13 × 13 ; 256 = 16 × 16 . Not square numbers- 20 , 27 , 50 , 75 , 108 , 180 . The least positive integer which when multiplied by the given number gives a square number- ⇒ 20 : - 20 by 5 ⇒ 27 : - 27 by 3 ⇒ 50 : - 50 by 2 ⇒ 75 : - 75 by 3 ⇒ 108 : - 108 by 3 ⇒ 180 : - 180 by 5 Hence, the table is as follows; Square number Not square number What is the least positive integer which when multiplied by the given number gives a square number 100 = 10 × 10 144 = 12 × 12 169 = 13 × 13 256 = 16 × 16 20 27 50 75 108 180 20 : - 20 by 5 27 : - 27 by 3 50 : - 50 by 2 75 : - 75 by 3 108 : - 108 by 3 180 : - 180 by 5

Arrange the following in ascending order of their value. 36 + 25 , 49 + 9 , 25 + 100 , 4 + 16

Given, 36 + 25 , 49 + 9 , 25 + 100 , 4 + 16 to arrange in ascending order. Let us first simplify the given expressions one by one. 36 + 25 = 6 + 5 = 11 49 + 9 = 7 + 3 = 10 25 + 100 = 5 + 10 = 15 4 + 16 = 2 + 4 = 6 We know that, ascending order is a method of arranging numbers from smallest to largest. So, arranging the numbers in ascending order, we get, ⇒ 6 , 10 , 11 , 15 or 4 + 16 , 49 + 9 , 36 + 25 , 25 + 100 . Hence, the required arrangement of numbers in ascending order is 4 + 16 , 49 + 9 , 36 + 25 , 25 + 100 .

Let's find the similarity between the digits in the units place of an integer and square number. Integer Square Number a × a Unit place of square number 0 in units 10 , 20 , 30 . . . 100 , 400 , 900 . . . Unit place of square _____ 1 in units 11 , 21 , 31 . . . 121 , 441 , 961 . . . Unit place of square 1 2 in units 12 , 22 , 42 . . . 144 , _____ , _____ Unit place of square _____ 3 in units 13 , 23 , 53 . . . 169 , _____ , _____ Unit place of square _____ 4 in units 14 , 24 , 44 . . . 196 , _____ , 1936 . . . Unit place of square _____ 5 in units 15 , 25 , 35 . . . 225 , _____ , _____ Unit place of square _____ 6 in units 16 , 26 , 66 . . . 256 , _____ , _____ Unit place of square _____ 7 in units 17 , 27 , 57 . . . 289 , _____ , _____ Unit place of square _____ 8 in units 18 , 28 , 78 . . . 324 , _____ , _____ Unit place of square _____ 9 in units 19 , 29 , 39 . . . 361 , _____ , _____ Unit place of square _____

The given table is as follows, Integer Square Number a × a Unit place of square number 0 in units 10 , 20 , 30 . . . 100 , 400 , 900 . . . Unit place of square _____ 1 in units 11 , 21 , 31 . . . 121 , 441 , 961 . . . Unit place of square 1 2 in units 12 , 22 , 42 . . . 144 , _____ , _____ Unit place of square _____ 3 in units 13 , 23 , 53 . . . 169 , _____ , _____ Unit place of square _____ 4 in units 14 , 24 , 44 . . . 196 , _____ , 1936 . . . Unit place of square _____ 5 in units 15 , 25 , 35 . . . 225 , _____ , _____ Unit place of square _____ 6 in units 16 , 26 , 66 . . . 256 , _____ , _____ Unit place of square _____ 7 in units 17 , 27 , 57 . . . 289 , _____ , _____ Unit place of square _____ 8 in units 18 , 28 , 78 . . . 324 , _____ , _____ Unit place of square _____ 9 in units 19 , 29 , 39 . . . 361 , _____ , _____ Unit place of square _____ We know that, a square number or perfect square is an integer that is the square of an integer. So, now lets find the squares of the given numbers and then observe their unit's digit. Integer Square Number a × a Unit place of square number 0 in units 10 , 20 , 30 . . . 100 , 400 , 900 . . . Unit place of square 0 1 in units 11 , 21 , 31 . . . 121 , 441 , 961 . . . Unit place of square 1 2 in units 12 , 22 , 42 . . . 144 , 484 , 1764 . . . Unit place of square 4 3 in units 13 , 23 , 53 . . . 169 , 529 , 2809 . . . Unit place of square 9 4 in units 14 , 24 , 44 . . . 196 , 576 , 1936 . . . Unit place of square 6 5 in units 15 , 25 , 35 . . . 225 , 625 , 1225 . . . Unit place of square 5 6 in units 16 , 26 , 66 . . . 256 , 676 , 4356 . . . Unit place of square 6 7 in units 17 , 27 , 57 . . . 289 , 729 , 3249 . . . Unit place of square 9 8 in units 18 , 28 , 78 . . . 324 , 784 , 6084 . . . Unit place of square 4 9 in units 19 , 29 , 39 . . . 361 , 841 , 1521 . . . Unit place of square 1 We observe, the square numbers which has 0 in unit's place, their square value also has 0 in units. The square numbers which has 4 in unit's place, their square value has 6 in units. The square numbers which has 5 in unit's place, their square value has 5 in units. The square numbers which has 6 in unit's place, their square value has 6 in units. The square numbers which has 9 in unit's place, their square value has 1 in units.

HARD

6th West Bengal Board

IMPORTANT

Earn 100

Find the least square number other than $0$ which is divisible by $10, 15, 20$ and $30$ . Also write the next square number which will be divisible by these numbers.

Important Questions on Square Root

HARD

6th West Bengal Board

IMPORTANT

GANITPRABHA (MATHEMATICS TEXT BOOK) CLASS 6>Chapter 18 - Square Root>Let's Work out - 18.2>Q 5

Place the given numbers in the respective columns.

$20, 27, 50, 75, 100, 108, 144, 169, 180, 256$

Square number	Not square number	What is the least positive integer which when multiplied by the given number gives a square number

HARD

6th West Bengal Board

IMPORTANT

GANITPRABHA (MATHEMATICS TEXT BOOK) CLASS 6>Chapter 18 - Square Root>Let's Work out - 18.2>Q 6

This year on Netaji's birthday, the students present in physical education class were made to stand in rows of $18, 24, 27$ for march past. At one point of time we formed a solid square. Find the least number of students present in school on that day.

MEDIUM

6th West Bengal Board

IMPORTANT

GANITPRABHA (MATHEMATICS TEXT BOOK) CLASS 6>Chapter 18 - Square Root>Let's Work out - 18.2>Q 7

The product of two positive numbers is

147

. The greater number is

3

times the smaller number. Find the two numbers.

MEDIUM

6th West Bengal Board

IMPORTANT

GANITPRABHA (MATHEMATICS TEXT BOOK) CLASS 6>Chapter 18 - Square Root>Let's Work out - 18.2>Q 8

Arrange the following in ascending order of their value.

$(\sqrt{36} + \sqrt{25}), (\sqrt{49} + \sqrt{9}), (\sqrt{25} + \sqrt{100}), (\sqrt{4} + \sqrt{16})$

HARD

6th West Bengal Board

IMPORTANT

GANITPRABHA (MATHEMATICS TEXT BOOK) CLASS 6>Chapter 18 - Square Root>Let's Work out - 18.2>Q 9

Out of the three positive numbers, the product of, first and second is

24;

second and third is

48;

and that of first and third is

32

. Find the three numbers.

MEDIUM

6th West Bengal Board

IMPORTANT

GANITPRABHA (MATHEMATICS TEXT BOOK) CLASS 6>Chapter 18 - Square Root>Let's Work out - 18.2>Q 10

On Republic Day, our Physical Education teacher made all students stand in rows having

12, 15

and

20

students, at different point of time for march past. At one point of time, the students were arranged in solid square. Find at least how many students were present in school on that day.

HARD

6th West Bengal Board

IMPORTANT

GANITPRABHA (MATHEMATICS TEXT BOOK) CLASS 6>Chapter 18 - Square Root>Exercise 11

Let's find the similarity between the digits in the units place of an integer and square number.

	Integer	Square Number $(a \times a)$	Unit place of square number
$0$ in units	$10, 20, 30 . . .$	$100, 400, 900 . . .$	Unit place of square _____
$1$ in units	$11, 21, 31 . . .$	$121, 441, 961 . . .$	Unit place of square $1$
$2$ in units	$12, 22, 42 . . .$	$144,$ _____ $,$ _____	Unit place of square _____
$3$ in units	$13, 23, 53 . . .$	$169,$ _____ $,$ _____	Unit place of square _____
$4$ in units	$14, 24, 44 . . .$	$196,$ _____ $, 1936 . . .$	Unit place of square _____
$5$ in units	$15, 25, 35 . . .$	$225,$ _____ $,$ _____	Unit place of square _____
$6$ in units	$16, 26, 66 . . .$	$256,$ _____ $,$ _____	Unit place of square _____
$7$ in units	$17, 27, 57 . . .$	$289,$ _____ $,$ _____	Unit place of square _____
$8$ in units	$18, 28, 78 . . .$	$324,$ _____ $,$ _____	Unit place of square _____
$9$ in units	$19, 29, 39 . . .$	$361,$ _____ $,$ _____	Unit place of square _____

EASY

6th West Bengal Board

IMPORTANT

GANITPRABHA (MATHEMATICS TEXT BOOK) CLASS 6>Chapter 18 - Square Root>Exercise 12>Q -1

Number of digits in the square number is either double or

1

less than double of the number of digits in the given number.

Find the least square number other than 0 which is divisible by 10, 15, 20 and 30. Also write the next square number which will be divisible by these numbers.

Important Questions on Square Root

Learn and Prepare for any exam you want !

Find the least square number other than $0$ which is divisible by $10, 15, 20$ and $30$ . Also write the next square number which will be divisible by these numbers.