Sample QuestionsSquare and Square Roots questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
Which of the following can be the square of a natural number $'n\ ’?$
- A
Sum of the squares of first $n$ natural numbers.
- B
Sum of the first $n$ natural numbers.
- C
Sum of first $(n – 1)$ natural numbers.
- ✓
Sum of first $'n\ ’$ odd natural numbers.
Answer: D.
View full solution →The unit digit in the square of the number $1000$ is:
Answer: B.
View full solution →If $5278$ is squared, then what will be at unit place?
Answer: C.
View full solution →If $252 = 625$, then the square root of $625$ is:
Answer: B.
View full solution →What will be the number of zeros in the square of the number $100$?
Answer: B.
View full solution →Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion (A): The perfect square number out of $2, 3, 4$ and $5$ is $4.$
Reasons (R): A perfect square is a number that can be expressed as the product of an integer by itself or as the second exponent of an integer.
- ✓
Both $A$ and $R$ are true and $R$ is the correct explanation of $A$.
- B
Both $A$ and $R$ are true but $R$ is not the correct explanation of $A$.
- C
$A$ is true but $R$ is false.
- D
$A$ is false but $R$ is true.
Answer: A.
View full solution →Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion (A): The number of zeros in the square of the number $100$ is $4.$
Reasons (R): The number of zeros at the end of the number obtained, by multiplying the number from $1$ to $100$ will be.
- ✓
Both $A$ and $R$ are true and $R$ is the correct explanation of $A$.
- B
Both $A$ and $R$ are true but $R$ is not the correct explanation of $A$.
- C
$A$ is true but $R$ is false.
- D
$A$ is false but $R$ is true.
Answer: A.
View full solution →Directions: In the following questions, the Assertions $(A)$ and Reason$(s)$ $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion $(A)$: The number of zeros in the square of the number $9000$ is $6$.
Reasons $(R)$: The number of zeros at the end of the number obtained, by multiplying the number from $1$ to $100$ will be.
- ✓
Both $A$ and $R$ are true and $R$ is the correct explanation of $A$.
- B
Both $A$ and $R$ are true but $R$ is not the correct explanation of $A$.
- C
$A$ is true but $R$ is false.
- D
$A$ is false but $R$ is true.
Answer: A.
View full solution →Directions: In the following questions, the Assertions $(A)$ and Reason$(s)$ $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion $(A)$: The Square of the following numbers will be odd $81$.
Reasons $(R)$: An odd number is an integer when divided by two, either leaves a remainder or the result is a fraction.
- ✓
Both $A$ and $R$ are true and $R$ is the correct explanation of $A$.
- B
Both $A$ and $R$ are true but $R$ is not the correct explanation of $A$.
- C
$A$ is true but $R$ is false.
- D
$A$ is false but $R$ is true.
Answer: A.
View full solution →Directions: In the following questions, the Assertions $(A)$ and Reason$(s) (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion $(A)$: The unit digit in the square of the number $2644$ is $4$
Reasons $(R)$: Units digit of a number is the digit in the one’s place of the number. i.e. it is the rightmost digit of the number.
- A
Both $A$ and $R$ are true and $R$ is the correct explanation of $A$.
- B
Both $A$ and $R$ are true but $R$ is not the correct explanation of $A$.
- C
$A$ is true but $R$ is false.
- ✓
$A$ is false but $R$ is true.
Answer: D.
View full solution →There are $500$ children in a school. For a $P.T.$ drill they have to stands 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.
View full solution →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.
View full solution →In a right triangle $ABC$, $\angle B = 90^{\circ}$. If $AC = 13\ cm, BC = 5\ cm$, find $AB$.
View full solution →In a right triangle $ABC$, $\angle$$B = 90^\circ$. If $AB = 6\ cm, BC = 8\ cm$, find $AC$.
View full solution →Find the length of the side of a square where area is 441 $m^2$.
View full solution →Find the smallest square number that is divisible by each of the numbers $4, 9$ and $10.$
View full solution →$2025$ plants are to be planted in a garden in such a way that each row contains as many plants as the number of rows. Find the number of rows and the number of plants in each row.
View full solution →The students of Class $VIII$ of a school donated ₹ $2401$ for Prime Minister's 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.
View full solution →Find the square root of $100$ by the method of repeated subtraction.
View full solution →Find the square root of $169$ by the method of repeated subtraction.
View full solution →Find the least number which must be subtracted from $825$ so as to get a perfect square. Also find the square root of the perfect square so obtained.
View full solution →Find the least number which must be subtracted from $3250$ so as to get a perfect square. Also find the square root of the perfect square so obtained.
View full solution →Find the least number which must be subtracted from $1989$ so as to get a perfect square. Also find the square root of the perfect square so obtained.
View full solution →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.
View full solution →Find the square root of the following decimal numbers.$51.84$
View full solution →Find the square root of each of the following numbers by Division method.
$3249$
View full solution →Find the square root of the following decimal numbers.
$2.56$
View full solution →Find the square root of each of the following numbers by Division method. $529$
View full solution →Find the square root of each of the following numbers by Division method.$1024$
View full solution →Find the number of digits in the square root of $390625$ (without any calculation).
View full solution →Find the number of digits in the square root of $27225$ (without any calculation).
View full solution →Find the number of digits in the square root of $4489$ (without any calculation).
View full solution →Find the number of digits in the square root of $144$ (without any calculation).
View full solution →Find the number of digits in the square root of $64$ (without any calculation).
View full solution →The smallest $4-$digit square number is the square of$............(31, 32, 99)$
View full solution →If a perfect square is a $3-$digit or a $4-$digit number. then its squareroot will have............digits. $(1, 2, 3)$
View full solution →The square root of $3.61$ is$............ (1.7, 1.9, 2.1)$
View full solution →If a number ends in...........then it can be a perfect square. $(2, 3, 5)$
View full solution →If a number ends in............then it cannot be a perfect square. $(2, 4, 6)$
View full solution →