Which of the following cannot be a perfect square?
- A841
- B529
- ✓198
- DAll of these
Answer: C.
View full solution →Question types
Squares and Square Roots question types
186 questions across 10 question groups — pick any mix to generate a MATHS paper with step-by-step answer keys.
186
Questions
10
Question groups
5
Question types
01
M.C.Q. [1 Marks Each]
20 Q→02TRUE-FLASE [1 Marks Each]
5 Q→03Assertion (A) & Reason (B) MCQ
3 Q→042 Marks Questions
36 Q→053 Marks Question
19 Q→065 Marks Questions
5 Q→07MATCH THE FOLLOWING.
1 Q→081 Marks Question
90 Q→09BLANKS [1 Marks Each]
5 Q→104 Mark Question
2 Q→Sample Questions
Squares 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 is a square of an even number?
- ✓144
- B169
- C441
- D625
Answer: A.
View full solution →196 is the square of
- A11
- B12
- ✓14
- D16
Answer: C.
View full solution →The least number which must be subtracted from the number 1988, so as to get a perfect square is
- A41
- B42
- ✓52
- D54
Answer: C.
View full solution →Which of the following symmetric arrangement cannot be used to represent a squared number?
- A
- B
- ✓
- D
Answer: C.
View full solution →The sum of two perfect squares is a perfect square.
All numbers of a pythagorean triplet are odd.
The square of 2.3 is 2.59.
There is one square number between 160 and 170.
The square of 87 will have 3 at the unit place.
Assertion (A) 6838 is a perfect square number.
Reason (R) A perfect square number can never have 8 at unit place.
Reason (R) A perfect square number can never have 8 at unit place.
- ABoth A and R are true and R is the correct explanation of A.
- BBoth A and R are true but R is not the correct explanation of A.
- CA is true but R is false.
- ✓A is false but R is true.
Answer: D.
View full solution →Assertion (A) The square root of a non-perfect square is always irrational.
Reason (R) A non-perfect square is a number that cannot be expressed as the product of an integer by Itself. (e.g. $\sqrt{2}, \sqrt{5}$ or $\sqrt{7}$ )
Reason (R) A non-perfect square is a number that cannot be expressed as the product of an integer by Itself. (e.g. $\sqrt{2}, \sqrt{5}$ or $\sqrt{7}$ )
- ✓Both A and R are true and R is the correct explanation of A.
- BBoth A and R are true but R is not the correct explanation of A.
- CA is true but R is false.
- DA is false but R is true.
Answer: A.
View full solution →Assertion (A) The square root of a perfect square is always a whole number.
Reason (R) A perfect square is a number that can be expressed as the product of an integer by itself.
(e.g. $9=3 \times 3$ or $16=4 \times 4$)
Reason (R) A perfect square is a number that can be expressed as the product of an integer by itself.
(e.g. $9=3 \times 3$ or $16=4 \times 4$)
- ✓Both A and R are true and R is the correct explanation of A.
- BBoth A and R are true but R is not the correct explanation of A.
- CA is true but R is false.
- DA is false but R is true.
Answer: A.
View full solution →(i) If $11^2=121$, what is the square root of 121 ?
(ii) If $14^2=196$, what is the square root of $196 ?$
View full solution →(ii) If $14^2=196$, what is the square root of $196 ?$
Find the squares of the following numbers containing 5 in unit place.
(i) 15$\quad$(ii) 95$\quad$(iii) 105$\quad$(iv) 205
View full solution →(i) 15$\quad$(ii) 95$\quad$(iii) 105$\quad$(iv) 205
Can you find the square of the following numbers using the above pattern (from NCERT Page No. 57)?
(i) $6666667^2$$\quad$(ii) $66666667^2$
View full solution →Express the following as the sum of two consecutive integers.
(i) $21^2$ $\quad$ (ii) $13^2$ $\quad$ (iii) $11^2$$\quad$(iv) $19^2$
View full solution →(i) $21^2$ $\quad$ (ii) $13^2$ $\quad$ (iii) $11^2$$\quad$(iv) $19^2$
Find whether each of the following numbers is a perfect square or not.
(i) 121 $\quad$ (ii) 55 $\quad$ (iii) 81 $\quad$ (iv) 49 $\quad$ (v) 69
View full solution →(i) 121 $\quad$ (ii) 55 $\quad$ (iii) 81 $\quad$ (iv) 49 $\quad$ (v) 69
By repeated subtraction of odd number starting from 1, find whether the following numbers are perfect squares or not. If the number is a perfect square, then find its square root.
(i) 121$\quad$(ii) 55$\quad$(iii) 36$\quad$(iv) 49$\quad$(v) 90
View full solution →(i) 121$\quad$(ii) 55$\quad$(iii) 36$\quad$(iv) 49$\quad$(v) 90
What will be the ones digit in the square of the following numbers?
(i) 1234 $\quad$ $\quad$(ii) 26387 $\quad$ (iii) 52698
(iv) 99880 $\quad$ (v) 21222 $\quad$ (vi) 9106
View full solution →(i) 1234 $\quad$ $\quad$(ii) 26387 $\quad$ (iii) 52698
(iv) 99880 $\quad$ (v) 21222 $\quad$ (vi) 9106
Which of the following numbers would have digit 6 at unit place?
(i) $19^2$ $\quad$ (ii) $24^2$ $\quad$ (iii) $26^2$
(iv) $36^2$$\quad$(v) $34^2$
View full solution →(i) $19^2$ $\quad$ (ii) $24^2$ $\quad$ (iii) $26^2$
(iv) $36^2$$\quad$(v) $34^2$
(i) $(-1)^2=1$. Is -1, a square root of 1?
(ii) $(-2)^2=4$. Is -2, a square root of 4?
(iii) $(-9)^2=81$. Is -9, a square root of 81?
View full solution →(ii) $(-2)^2=4$. Is -2, a square root of 4?
(iii) $(-9)^2=81$. Is -9, a square root of 81?
In a right angled $\triangle \text{ABC}, \angle \text{B}=90^{\circ}$.
(i) If $\text{AB}=6 \text{ cm}$ and $\text{BC}=8 \text{ cm}$, find $\text{AC}$.
(ii) If $\text{AC}=13 \text{ cm}$ and $\text{BC}=5 \text{ cm}$, find $\text{AB}$.
View full solution →(i) If $\text{AB}=6 \text{ cm}$ and $\text{BC}=8 \text{ cm}$, find $\text{AC}$.
(ii) If $\text{AC}=13 \text{ cm}$ and $\text{BC}=5 \text{ cm}$, find $\text{AB}$.
The perimeters of two squares are 40 m and 96 m, respectively. Find the perimeter of another square, equal in area to the sum of the first two squares.
During a mass drill exercise, 6250 students of different schools are arranged in rows such that the number of students in each row is equal to the number of rows. In doing so, the instructor finds out that 9 children are left out. Find the number of children in each row of the square.
Find the square root of 324 by the method of repeated subtraction.
Find the least number that must be added to 1500, so as to get a perfect square. Also, find the square root of the perfect square.
A ladder 10 m long rests against a vertical wall. If the foot of the ladder is 6 m away from the wall and the ladder just reaches the top of the wall, how high is the wall?
| Column A (Number) | Column B (Square root) |
| (a) 4.41 | (i) 1.4 |
| (b) 2.89 | (ii) 0.9 |
| (c) 0.81 | (iii) 1.7 |
| (d) 1.96 | (iv) 2.1 |
Without calculating square root, find the number of digits in the square root of the following numbers.
(i) 36864
(i) 36864
Without calculating square root, find the number of digits in the square root of the following numbers.
(i) 100000000
(i) 100000000
Without calculating square root, find the number of digits in the square root of the following numbers.
(i) 25600
(i) 25600
Write the square, making use of the above pattern (from NCERT Page No. 57).
(i) $111111^2$$\quad$(ii) $1111111^2$
View full solution →(i) $111111^2$$\quad$(ii) $1111111^2$
Do you think the reverse is also true l.e. Is the sum of any two consecutive positive Integers is perfect square of a number? Give example to support your answer.
The least number by which 125 be multiplied to make it a perfect square is _____________.
The square of 0.9 is _____________
$\sqrt{2.89}=$ _____________.
View full solution →The square root of 24025 will have _____________ digits.
The unit digit in the square of 1456 is _____________.
For each of the following numbers, find the smallest whole number by which it should be multiplied, so as to get a perfect square number. Also, find the square root of the square number, so obtained.
108
108
For each of the following numbers, find the smallest whole number by which it should be multiplied, so as to get a perfect square number. Also, find the square root of the square number, so obtained.
252
252
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