Sample QuestionsSquares 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.
Tick $(\checkmark)$ the correct answer of the following: $\sqrt{0.9}\times\sqrt{1.6}=\ ?$
- A
$0.12$
- B
$1.2$
- ✓
$0.75$
- D
$12$
Answer: C.
View full solution →Tick $(\checkmark)$ the correct answer of the following: Which of the following is a pythagorean triplet$?$
- A
$(2, 3, 5)$
- ✓
$(5, 7, 9)$
- C
$(6, 9, 11)$
- D
$(8, 15, 17)$
Answer: B.
View full solution →Mark $(\checkmark)$ against the correct answer $\sqrt{2\frac{1}{4}}=\ ?$
- A
$2\frac{1}{2}$
- B
$1\frac{1}{4}$
- ✓
$1\frac{1}{2}$
- D
Answer: C.
View full solution →Tick $(\checkmark)$ the correct answer of the following: The square of a proper fraction is:
- A
Larger than the fraction.
- ✓
Smaller than the fraction.
- C
- D
Answer: B.
View full solution →Tick $(\checkmark)$ the correct answer of the following: Which of the following numbers is not a perfect square$?$
Hint: The number $81000$ ends in an odd number of zeros.
- A
$3600$
- B
$6400$
- ✓
$81000$
- D
$2500$
Answer: C.
View full solution →Assertion (A): For positive values of a rational number $n, n^2>n$ only if $n>1$.
Reason (R): For $0<n<1$, we have $n^2<n$.
- ✓
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
- B
Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).
- C
Assertion (A) is true but Reason (R) is false.
- D
Assertion (A) is false but Reason (R) is true.
Answer: A.
View full solution →Assertion (A): Since 9 is a perfect square, so each one of 0.9, 0.09, 0.009, 0.0009 is a perfect square.
Reason (R): $0.9=\frac{9}{10}, 0.09=\frac{9}{100}, 0.009=\frac{9}{1000}, 0.0009=\frac{9}{10000}$.
- A
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
- B
Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).
- C
Assertion (A) is true but Reason (R) is false.
- ✓
Assertion (A) is false but Reason (R) is true.
Answer: D.
View full solution →Assertion (A): The square of a prime number may be prime or composite.
Reason (R): The square of a number can never be prime.
- A
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
- B
Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).
- C
Assertion (A) is true but Reason (R) is false.
- ✓
Assertion (A) is false but Reason (R) is true.
Answer: D.
View full solution →Assertion (A): $\left(\frac{3}{4}\right)^2<\frac{3}{4}$
Reason (R) : The square of a proper fraction is smaller than the fraction.
- ✓
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
- B
Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).
- C
Assertion (A) is true but Reason (R) is false.
- D
Assertion (A) is false but Reason (R) is true.
Answer: A.
View full solution →Assertion (A): A number ending in 2, 3, 7 or 8 is never a perfect square.
Reason (R): None of the numbers from 1 to 9 when squared ends in 2, 3, 7 or 8 .
- ✓
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
- B
Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).
- C
Assertion (A) is true but Reason (R) is false.
- D
Assertion (A) is false but Reason (R) is true.
Answer: A.
View full solution →By what least number should the given number be multiplied to get a perfect square number? In case, find the number whose square is the new number. $7623$
View full solution →Using the prime factorisation method, find the following numbers are perfect squares: $441$
View full solution →By what least number should the given number be multiplied to get a perfect square number$?$ In case, find the number whose square is the new number. $2925$
View full solution →By what least number should the given number be multiplied to get a perfect square number$?$ In case, find the number whose square is the new number. $3380$
View full solution →Find the largest number of $2$ digits which is a perfect square.
View full solution →Find the smallest number by which $2925$ must be divided to obtain a perfect square. Also, find the square root of the perfect square so obtained.
View full solution → Evaluate $\sqrt{0.9}$ correct up to two places of decimal.
View full solution →Find the least number which must be added to $8400$ to obtain a perfect square. Find this perfect square and its square root.
View full solution →Find the greatest number of five digits which is a perfect square. What is the square root of this number$?$
View full solution →Find the least square number which is exactly divisible by each of the numbers $8, 12, 15$ and $20.$
View full solution →The students of a class arranged a picnic. Each student contributed as many rupees as the number of students in the class. If the total contribution is $Rs. 1156,$ find the strength of the class.
View full solution →Find the length of each side of a square whose area is equal to the area of a rectangle of length $13.6$ metres and breadth $3.4$ metres.
View full solution →$1225$ 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 →There are $m$ boys and $n$ girls in a class. Each boy donated twice as many rupees as is the total number of boys and each girl donated thrice as many rupees as is the total number of girls. The boys collected ₹1152 in all while the girls collected ₹768 in all.
(1) What is the value of $m$ ?
(a) 22$\quad$(b) 24$\quad$(c) 26$\quad$(d) 28
(2) What is the value of $n$ ?
(a) 12$\quad$(b) 14$\quad$(c) 16$\quad$(d) 18
(3) Had there been $(m+3)$ boys and $(n-3)$ girls in the class, the total amount collected would be
(a) ₹ 1925$\quad$(b) ₹ 1940(c) ₹ 1965$\quad$(d) ₹ 2000
(4) Let $p=m^2+n^2$. Then, which of the following is true for $p$ ?
(a) $p$ is a perfect square.(b) $(p+9)$ is a perfect square.(c) $(p+2)$ is a perfect square.(d) $(p-32)$ is a perfect square.
(5) Let $q=m^2-n^2$. Then, the least number to be added to $q$ to make it a perfect square is
(a) 4(b) 6(c) 8(d) 12
View full solution →Which of the following are squares of even numbers?
$900$
View full solution →Fill in the blank: The square of a proper fraction is __________ than the given fraction.
Without adding, find the sum:
$(1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19)$
View full solution →Write $(T)$ for true and $(F)$ for false for the statement given below: The difference of two perfect squares is a perfect square.
View full solution →Fill in the blank. $\sqrt{1681}=\ .......$
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