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Maths Solve The Following Question.1MARKS

Squares and Square Roots · Maharashtra Board STD 8 (MSBSHSE - Semi English Medium). 33 questions.

Questions

Solve The Following Question.1MARKS

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33 questions · self-marked practice — reveal the answer and mark yourself.

Question 11 Mark
Which of the following are squares of even numbers?
$900$
Answer
We know that the square of an odd number is odd and square of an even number is even.

900 is even $\Rightarrow(900)^2$ is even.
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Question 21 Mark
Fill in the blank:
The square of a proper fraction is __________ than the given fraction.
Answer
The square of a proper fraction is less than the given fraction.
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Question 31 Mark
Without adding, find the sum:
$(1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19)$
Answer
Sum of first 10 odd numbers $=10^2=100$.
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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.
Answer
False.
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Question 51 Mark
Fill in the blank.
$\sqrt{1681}=\ .......$
Answer
$\sqrt{1681}=41$Solution:
$\begin{array}{c|c}&41\\\hline4&\overline{16}\ \overline{81}\\4&16\ \ \ \ \ \ \\\hline81&\ \ \ \ 81\\\ \ \ \ 1&\ \ \ \ 81\\\hline&\ \ \ \ 0\\\end{array}$
$\sqrt{1681}=41$
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Question 61 Mark
Which of the following are squares of odd numbers?
961
Answer
According 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.
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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.
Answer
True.
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Question 81 Mark
Fill in the blank:
$n ^2=$ the sum of first n $\qquad$ natural numbers.
Answer
$n ^2=$ = the sum of first n odd natural numbers.
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Question 91 Mark
Write (T) for true and (F) for false for the statement given below:
The square of a prime number is prime.
Answer
False.
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Question 101 Mark
Which of the following are squares of odd numbers?
7396
Answer
According 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.
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Question 111 Mark
Fill in the blank.
The smallest square number exactly divisible by 2, 4, 6 is _______.
Answer
The smallest square number exactly divisible by 2, 4, 6 is 36.Solution:
LCM of 2, 4 and 6 is 12. Prime factorisation of 12 = 2 × 2 × 3 To make it a perfect square, we need to multiply it by 3. $\therefore$ 12 × 3 = 36
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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.
Answer
A 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.
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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.
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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.
Answer
False.
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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.
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Question 161 Mark
Without adding, find the sum:
$(1 + 3 + 5 + 7 + 9 + 11 + 13)$
Answer
Sum of first 6 odd numbers $=7^2=49$.
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Question 171 Mark
Which of the following are squares of even numbers?
$441$
Answer
We know that the square of an odd number is odd and square of an even number is even.

441 is odd $\Rightarrow(441)^2$ is odd.
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Question 181 Mark
Which of the following are squares of odd numbers?
484
Answer
According 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.
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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.
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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.
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Question 211 Mark
Which of the following are squares of odd numbers?
8649
Answer
According 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.
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Question 221 Mark
Which of the following are squares of even numbers?
$625$
Answer
We know that the square of an odd number is odd and square of an even number is even.

625 is odd $\Rightarrow(625)^2$ is odd.
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Question 231 Mark
Without adding, find the sum:
$(1+3+5+7+9+11+13+15+17+19+21+23)$
Answer
Sum of first 12 odd numbers $=12^2=144$.
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Question 241 Mark
Which of the following are squares of even numbers?
$324$
Answer
We know that the square of an odd number is odd and square of an even number is even.

324 is even $\Rightarrow(324)^2$ is even.
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Question 261 Mark
Which of the following are squares of odd numbers?
4225
Answer
According 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.
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Question 281 Mark
Fill in the blank:
The square of an even number is __________.
Answer
The square of an even number is even.
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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.
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Question 301 Mark
Which of the following are squares of even numbers?
$196$
Answer
We know that the square of an odd number is odd and square of an even number is even.

196 is even $\Rightarrow(196)^2$ is even.
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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.
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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.
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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.
Answer
False.
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