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All questions of Squares & Square Roots for Class 8 Exam
What is the greatest number of four digits which is a perfect square?- a)9801
- b)9816
- c)9824
- d)9864
Correct answer is option 'A'. Can you explain this answer?
What is the greatest number of four digits which is a perfect square?
a)
9801
b)
9816
c)
9824
d)
9864
 | Pie Academy answered |
Greatest number of four digits = 9999
The perimeter of a square field is 76m. What is its area?- a)324 m2
- b)289 m2
- c)361 m2
- d)329 m2
Correct answer is option 'C'. Can you explain this answer?
The perimeter of a square field is 76m. What is its area?
a)
324 m2
b)
289 m2
c)
361 m2
d)
329 m2
 | Shubham Sharma answered |
Perimeter of square = 76
⇒ 4 × side = 76 ⇒ side = 76/4 = 19
∴ Area of square = 192 = 361 m2
⇒ 4 × side = 76 ⇒ side = 76/4 = 19
∴ Area of square = 192 = 361 m2
What is the length of the diagonal of a square whose perimeter is equal to the perimeter of an equilateral triangle of side 4 cm?- a)4. 24 cm
- b)4.04 cm
- c)4.14 cm
- d)4.64
Correct answer is option 'A'. Can you explain this answer?
What is the length of the diagonal of a square whose perimeter is equal to the perimeter of an equilateral triangle of side 4 cm?
a)
4. 24 cm
b)
4.04 cm
c)
4.14 cm
d)
4.64
 | Amit Sharma answered |
Perimeter of an equilateral triangle
= 4 + 4 + 4 = 12 cm
Perimeter of square = 12 cm ⇒ 4 × side = 12 ⇒ Side = 3 cm.
∴ Length of diagonal =
= 4 + 4 + 4 = 12 cm
Perimeter of square = 12 cm ⇒ 4 × side = 12 ⇒ Side = 3 cm.
∴ Length of diagonal =
Which of the following is the square of an even number?- a)729
- b)324
- c)441
- d)625
Correct answer is option 'B'. Can you explain this answer?
Which of the following is the square of an even number?
a)
729
b)
324
c)
441
d)
625
 | Kavya Saxena answered |
Here 729 = 272, 324 = 182, 441 = 212, 625 = 252
or
Square of an odd number is an odd number.
or
Square of an odd number is an odd number.
By what least number 384 be multiplied so that the product may be a perfect square?- a)2
- b)5
- c)4
- d)6
Correct answer is option 'D'. Can you explain this answer?
By what least number 384 be multiplied so that the product may be a perfect square?
a)
2
b)
5
c)
4
d)
6
| | Ananya Das answered |
∴ 384 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3
so it lacks a 2 and 3
∴ Required number = 6
The area of a square field is 60025 m2. A man cycles along its boundary at 18 km/hour. In how much time will he return to the starting point?- a)166 seconds
- b)176 seconds
- c)196 Seconds
- d)None of these
Correct answer is option 'C'. Can you explain this answer?
The area of a square field is 60025 m2. A man cycles along its boundary at 18 km/hour. In how much time will he return to the starting point?
a)
166 seconds
b)
176 seconds
c)
196 Seconds
d)
None of these
| | Kavya Saxena answered |
Speed of cycle = 18 km/hour
18 x 5/18
5m/sec
Area of square = 60025
Side of square =
= 245 m
Perimeter of square = 245 × 4 m
∴ Time taken =
18 x 5/18
5m/sec
Area of square = 60025
Side of square =
= 245 mPerimeter of square = 245 × 4 m
∴ Time taken =
Find the smallest number by which 396 must be multiplied so that the product becomes a perfect square?- a)3
- b)5
- c)9
- d)11
Correct answer is option 'D'. Can you explain this answer?
Find the smallest number by which 396 must be multiplied so that the product becomes a perfect square?
a)
3
b)
5
c)
9
d)
11
| | Shubham Sharma answered |
396 = 2 × 2× 3 × 3 × 11
To make a perfect square, 11 is multiplied to 396.
To make a perfect square, 11 is multiplied to 396.
What is the length of each side of a square whose area is equal to the area of a rectangle of length 13.6 m and breadth 3.4 meters?- a)4.8 m
- b)5.8 m
- c)6.8 m
- d)7.8 cm
Correct answer is option 'C'. Can you explain this answer?
What is the length of each side of a square whose area is equal to the area of a rectangle of length 13.6 m and breadth 3.4 meters?
a)
4.8 m
b)
5.8 m
c)
6.8 m
d)
7.8 cm
 | Geetika Shah answered |
Area of square = Area of rectangle
∴ Side of square =
= 6.8 m
∴ Side of square =
= 6.8 mFind the smallest number by which 557568 must be divided so that it become a perfect square.- a)6
- b)4
- c)3
- d)2
Correct answer is option 'D'. Can you explain this answer?
Find the smallest number by which 557568 must be divided so that it become a perfect square.
a)
6
b)
4
c)
3
d)
2
 | Trisha Vashisht answered |
To determine the smallest number by which 557568 must be divided so that it becomes a perfect square, let's factorize 557568 and see the prime factors:
Step 1: Factorize 557568
We can start by dividing 557568 by the smallest prime numbers:
557568÷2=278784(Divide by 2)
278784÷2=139392(Divide by 2)
139392÷2=69696(Divide by 2)
69696÷2=34848(Divide by 2)
34848÷2=17424(Divide by 2)
17424 ÷ 2=8712(Divide by 2)
8712 ÷ 2 = 4356(Divide by 2)
4356÷2=2178(Divide by 2)
2178÷2=1089(Divide by 2, but can’t divide further, stop here with 1089)
To make this exponent even, we must divide by 2 to reduce the exponent to 8 (which is even). Hence, the smallest number by which 557568 should be divided to make it a perfect square is 2.
Answer: 4. 2
Which of the following is not a Pythagorean triplet?- a)(3, 4, 5)
- b)(6, 8, 10)
- c)(2, 3, 4)
- d)(12, 35, 37)
Correct answer is option 'C'. Can you explain this answer?
Which of the following is not a Pythagorean triplet?
a)
(3, 4, 5)
b)
(6, 8, 10)
c)
(2, 3, 4)
d)
(12, 35, 37)
| | Aditya Shah answered |
Here 32 + 42 = 52
62 + 82 = 102
22 + 32 ≠ 42
122 + 352 = 372
∴ (c) is not a Pythagorean triplet.
62 + 82 = 102
22 + 32 ≠ 42
122 + 352 = 372
∴ (c) is not a Pythagorean triplet.
Find the smallest square number that is divisible by each of the number 8, 15 and 20.- a)900
- b)1600
- c)2500
- d)3600
Correct answer is option 'D'. Can you explain this answer?
Find the smallest square number that is divisible by each of the number 8, 15 and 20.
a)
900
b)
1600
c)
2500
d)
3600
| | Shubham Sharma answered |
Here LCM of 8, 15, 20 = 120. and
120 = 2 × 2 × 2 × 3 × 5
To make 120 a perfect square, it must be multiplied by 2 × 3 ×5 = 30
120 × 30 = 3600
120 = 2 × 2 × 2 × 3 × 5
To make 120 a perfect square, it must be multiplied by 2 × 3 ×5 = 30
120 × 30 = 3600
The area of a rectangular field whose length is three times its breadth is 348 m2. What is the perimeter of the field?- a)82.16 m
- b)84.16 m
- c)86.16 m
- d)None of these
Correct answer is option 'C'. Can you explain this answer?
The area of a rectangular field whose length is three times its breadth is 348 m2. What is the perimeter of the field?
a)
82.16 m
b)
84.16 m
c)
86.16 m
d)
None of these
| | Geetika Shah answered |
Let breadth be x m
∴ Length = 3x m
Now
∴
Perimeter = 2 (10.77 + 32.31) = 86.16 m
∴ Length = 3x m
Now
∴
Perimeter = 2 (10.77 + 32.31) = 86.16 m
What is the least number which must be added to 6203 to obtain a perfect square ?- a)32
- b)34
- c)36
- d)38
Correct answer is option 'D'. Can you explain this answer?
What is the least number which must be added to 6203 to obtain a perfect square ?
a)
32
b)
34
c)
36
d)
38
| | Shubham Sharma answered |
6241 – 6203 = 38
38 must be added to 6203 to make a perfect square.
What is the smallest number of four digits which is a perfect square?- a)1016
- b)1024
- c)1036
- d)1048
Correct answer is option 'B'. Can you explain this answer?
What is the smallest number of four digits which is a perfect square?
a)
1016
b)
1024
c)
1036
d)
1048
 | Saanvi Kaur answered |
The smallest four digit no. = 1000
32^2 is more than 1000 by 24;
So the least number to be added to 1000 is 24.
Therefore, 1000+24 = 1024 is the smallest four digit number which is a perfect square.
What is the greatest number of five digits which is a perfect square?- a)99586
- b)99 856
- c)99568
- d)99865
Correct answer is option 'B'. Can you explain this answer?
What is the greatest number of five digits which is a perfect square?
a)
99586
b)
99 856
c)
99568
d)
99865
| | Anand Chawla answered |
The greatest number of five digits
and one of them is three times the other. Find the larger number.
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