Question 11 Mark
Which of the following are squares of even numbers?
$900$
AnswerWe know that the square of an odd number is odd and square of an even number is even.
$900$ is even ⇒ $(900)^2$ is even.
View full question & answer→Question 21 Mark
Fill in the blank: The square of a proper fraction is __________ than the given fraction.
AnswerThe square of a proper fraction is less than the given fraction.
View full question & answer→Question 31 Mark
Without adding, find the sum:
$(1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19)$
AnswerSum of first 10 odd numbers $= 10^2 = 100$.
View full question & answer→Question 41 Mark
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 question & answer→Question 51 Mark
Fill in the blank. $\sqrt{1681}=\ .......$
Answer$\sqrt{1681}=41$Solution:
$\begin{array}{c|c}&41\\\hline4&\overline{16}\ \overline{81}\\4&16\ \ \ \ \ \ \\\hline81&\ \ \ \ 81\\\ \ \ \ 1&\ \ \ \ 81\\\hline&\ \ \ \ 0\\\end{array}$
$\sqrt{1681}=41$
View full question & answer→Question 61 Mark
Which of the following are squares of odd numbers$?\ 961$
AnswerAccording to the property of squares, the square of an odd number is also an odd number Using this property, we will determine which of the numbers in the given list of squares is a square of an odd number.
$961$
This is an odd number. Thus, it is a square of an odd number.
View full question & answer→Question 71 Mark
Write $(T)$ for true and $(F)$ for false for the statement given below: The product of two perfect squares is a perfect square.
View full question & answer→Question 81 Mark
Fill in the blank:
$n^2 =$ the sum of first $n $_____ natural numbers.
Answer$n^2= $ the sum of first $n$ odd natural numbers.
View full question & answer→Question 91 Mark
Write $(T)$ for true and $(F)$ for false for the statement given below: The square of a prime number is prime.
View full question & answer→Question 101 Mark
Which of the following are squares of odd numbers$?$
$7396$
AnswerAccording to the property of squares, the square of an odd number is also an odd number Using this property, we will determine which of the numbers in the given list of squares is a square of an odd number.
$7396$
This is an even number. Thus, it is not a square of an odd number.
View full question & answer→Question 111 Mark
Fill in the blank. The smallest square number exactly divisible by $2, 4, 6$ is _______.
Answer$LCM$ of $2,4$ and $6$ is $12.$ Prime factorisation of $12 = 2 \times 2 \times 3$ To make it a perfect square, we need to multiply it by $3.$
$\therefore 12 \times 3 = 36$
View full question & answer→Question 121 Mark
Fill in the blank. A given number is a perfect square having n digits, where n is odd. Then, its square root will have ______ digits.
AnswerA given number is a perfect square having n digits, where n is odd. Then, its square root will have $\Big(\frac{\text{n+1}}{2}\Big)$ digits.
View full question & answer→Question 131 Mark
Give reason to show that none of the numbers given below is a perfect square: $9468$
Answer$9468$ is not a perfect square, because the numbers end with $8,$ which is not a perfect square.
View full question & answer→Question 141 Mark
Write $(T)$ for true and $(F)$ for false for the statement given below: The sum of two perfect squares is a perfect square.
View full question & answer→Question 151 Mark
Give reason to show that none of the numbers given below is a perfect square: $8457$
Answer$8457$ is not a perfect square, because the numbers end with $7,$ which is not a perfect square.
View full question & answer→Question 161 Mark
Without adding, find the sum:
$(1 + 3 + 5 + 7 + 9 + 11 + 13)$
AnswerSum of first 6 odd numbers $= 7^2 = 49$.
View full question & answer→Question 171 Mark
Which of the following are squares of even numbers?
$441$
AnswerWe know that the square of an odd number is odd and square of an even number is even.
$441$ is odd ⇒ $(441)^2$ is odd.
View full question & answer→Question 181 Mark
Which of the following are squares of odd numbers$?\ 484$
AnswerAccording to the property of squares, the square of an odd number is also an odd number Using this property, we will determine which of the numbers in the given list of squares is a square of an odd number.
$484$
This is an even number. Thus, it is not a square of an odd number.
View full question & answer→Question 191 Mark
Give reason to show that none of the numbers given below is a perfect square: $5963$
Answer$5963$ is not a perfect square, because the numbers end with $3,$ which is not a perfect square.
View full question & answer→Question 201 Mark
Give reason to show that none of the numbers given below is a perfect square: $5372$
Answer$5372$ is not a perfect square, because the numbers end with $2,$ which is not a perfect square.
View full question & answer→Question 211 Mark
Which of the following are squares of odd numbers$?$
$8649$
AnswerAccording to the property of squares, the square of an odd number is also an odd number Using this property, we will determine which of the numbers in the given list of squares is a square of an odd number.
$8649$
This is an odd number. Thus, it is a square of an odd number.
View full question & answer→Question 221 Mark
Which of the following are squares of even numbers?
$625$
AnswerWe know that the square of an odd number is odd and square of an even number is even.
$625$ is odd ⇒ $(625)^2$ is odd.
View full question & answer→Question 231 Mark
Without adding, find the sum:
$(1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23)$
AnswerSum of first $12$ odd numbers
$= 12^2 = 144.$
View full question & answer→Question 241 Mark
Which of the following are squares of even numbers?
$324$
AnswerWe know that the square of an odd number is odd and square of an even number is even.
$324$ is even ⇒ $(324)^2$ is even.
View full question & answer→Question 251 Mark
Fill in the blank.
$1 + 3 + 5 + 7 + 9 + 11 + 13 $= (_______)$^2$.
Answer$1 + 3 + 5 + 7 + 9 + 11 + 13 = (7)^2$
View full question & answer→Question 261 Mark
Which of the following are squares of odd numbers$?\ 4225$
AnswerAccording to the property of squares, the square of an odd number is also an odd number Using this property, we will determine which of the numbers in the given list of squares is a square of an odd number.
$4225$
This is an odd number. Thus, it is a square of an odd number.
View full question & answer→Question 271 Mark
Fill in the blank: The square of an odd number is _________.
AnswerThe square of an odd number is odd.
View full question & answer→Question 281 Mark
Fill in the blank: The square of an even number is __________.
AnswerThe square of an even number is even.
View full question & answer→Question 291 Mark
Give reason to show that none of the numbers given below is a perfect square: $360$
Answer$360$ is not a perfect square, because the numbers ending in an odd number of zero, which is never a perfect square.
View full question & answer→Question 301 Mark
Which of the following are squares of even numbers?
$196$
AnswerWe know that the square of an odd number is odd and square of an even number is even.
$196$ is even ⇒ $(196)^2$ is even.
View full question & answer→Question 311 Mark
Give reason to show that none of the numbers given below is a perfect square: $2500000$
Answer$2500000$ is not a perfect square, because the numbers ending in an odd number of zero, which is never a perfect square.
View full question & answer→Question 321 Mark
Give reason to show that none of the numbers given below is a perfect square: $64000$
Answer$64000$ is not a perfect square, because the numbers ending in an odd number of zero, which is never a perfect square.
View full question & answer→Question 331 Mark
Write $(T)$ for true and $(F)$ for false for the statement given below: The number of digits in a perfect square is even.
View full question & answer→