Introduction to Square Numbers

Q.

Find the greatest number of two digits which is a perfect sqaure.

Q.

Fnd the least number of three digits which is perfect square.

Q.

Find the squares of the following numbers using column method. Verify the result by finding the square using the usual multiplication:
(i) 25 (ii)37
(iii)54 (iv)71
(v)96

Q. The smallest number by which 7623 must be divided to get a perfect square is .

1. 7
2. 9
3. 11

Q. The greatest 5 digit perfect square number is .

1. 99856
2. 99525
3. 99256
4. 99552

Q. Is $2352$ a perfect square ? If not, find the greater number closest to $2352$, which is a perfect square. Find the square root of the new number.

1. Yes, $2352$ a perfect square.
2. No, $2352$ is not a perfect square else $2304$ is closest perfect square.
   Square root of $2304is48$
   
3. No, $2352$ is not a perfect square else $2401$ is closest perfect square.
   Square root of $2401is49$
4. Data insufficient
   

Q.

What is the difference between the fraction and rational numbers?

Q.

Give reason to show that none of the numbers, given below, is a perfect square.

(i) 2162 (ii) 6843

(iii) 9637 (iv) 6598

Q. Hence, Find the greatest 3 digit number which is a perfect square

Q. The square of a proper frcation is
(a) larger than the fraction
(b) smaller than the fraction
(c) equal to the frcation
​​​​​​​(d) none of these

Q.

What is the least number that should be subtracted from $1385$ to get a perfect square? Also find the square root of the perfect square.

Q.

Without doing any calculation, find the numbers which are surely not perfect squares.

(i) 153 (ii) 257

(iii) 408 (iv) 441

Q. If a natural number 'm' can be expressed as $n^2$, where n is also a natural number , then m is called a

1. negative number
2. natural number
3. rational number
4. square number

Q.

Which of the following is a square of an even number?

1. $144$

2. $169$

3. $441$

4. $625$

Q.

Question 3 (iv)
Find the square root of the following decimal numbers:

42.25

Q.

Which of the following is not a perfect square?

1. 169

2. 196

3. 144

4. 245

Q.

What is the value of $\sqrt{77}$?

Q.

The square of $-9$ is

Q.

Question 15

Write the correct answer from the given four options.

The next two numbers in the number pattern 1, 4, 9, 16, 25, .... are

a) 35, 48
b) 36, 49
c) 36, 48
d) 35, 49

Q. If a natural number 'n' is added n times, we get .

1. $n^2$
2. $n^n$
3. n+n
4. 3n

Q.

The $222000$ number is not a perfect square. Give reason.

Q.

Find the least number which must be added to 6041 to get a perfect square.

Q. 3m square+24m+36

Q.

Which of the following is/are not a square number?

(i) 48
(ii) 1653
(iii) 121
(iv) 627

1. (i), (ii), (iii)

2. (i), (ii), (iv)

3. (iii)

4. All of them

Q.

The number of students joining a class 20 minutes back is 729. If the number of students joining the class triples every 10 minutes, what is the cube root of the number of students joining after 40 minutes from now?

1. 81

2. 64

3. 27

4. 48

Q. 125 cube * 729cube root

Q. Perfect square always ends with _____________ .

1. 0, 2, 3 or 5
2. 1, 5, 7 or 6
3. 0, 1, 4, 5, 6 or 9
4. 2, 3, 7 or 8

Q.

Question 3 (i)
Find the square root of the following decimal numbers:
2.56

Q.

Question 6
Using the given pattern, find the missing numbers:
$1^2+2^2+2^2=3^2$
$2^2+3^2+6^2=7^2$
$3^2+4^2+{12}^2={13}^2$
$4^2+5^2+{\underset{–}{}}^2={21}^2$
$5^2+{\underset{–}{}}^2+{30}^2={31}^2$
$6^2+7^2+\underset{–}{}2=\underset{–}{}2$

Q.

Write the following rational numbers in ascending order: