A Square and Cube - 1 - Class 8 Maths Free MCQ Test with solutions

Any 6-digit number N satisfies 100000 ≤ N ≤ 999999. Taking cube roots gives ∛100000 ≈ 46.4 and ∛999999 ≈ 99.999. Hence the cube root of any 6-digit number lies between 46.4 and 99.999, so it must be a two-digit integer.

 we have 135 =  3 x 3 x 3 x 5

Grouping the prime factors of 135 into triples, we are left over with 5.
∴  135 is not a perfect cube
Now, [135]divided by5 = [ 3 x 3 x 3 x 5] divided by5
or  27 = 3 x 3 x 3
i.e. 27 is a perfect cube.
Thus, the required smallest number is 5

The volume of a cube is calculated by cubing its edge length. For an edge length of 2 cm, the volume is:

• Volume = edge length × edge length × edge length
• Volume = 2 cm × 2 cm × 2 cm
• Volume = 8 cubic centimetres (cm³)

First find the cube root of 800
800 = 8 × 100

Now, 100 is not a perfect cube, so its cube root is not a whole number.
Hence, the cube root of 800 is a decimal number, not a whole number
Therefore, we can say the cube root does not exist as a whole number.
So, Correct Option: B

392 = 2 × 2 × 2 × 7 × 7
Hence the number should be multiplied by 7 to make it a perfect cube.

The cube of an even number is always an even number. Here's why:

To find the value of 729729729, we check cube powers:

The cube of an odd number is always an odd number because:

If the unit digit is 7, the cube will have unit digit as 7×7×7 = 343

So, the unit digit will be 3.

To determine which of the following numbers is not a perfect cube, we need to check whether the number can be expressed as the cube of an integer.

• a) 1 is a perfect cube because 1=1³.
• b) 9 is not a perfect cube. The cube root of 9 is not an integer.
• c) 8 is a perfect cube because 8 = 2³.
• d) 27 is a perfect cube because 27 = 3³.

Thus, the number that is not a perfect cube is:

b) 9.

The cube of 4 is:

Option 1:
√576 = 24

Option 2:
√841 = 29

Option 3:
√778 = 27.89 It is not perfect square

Option D:
√529 = 23

Hence, the answer is option C.

Let the other number be x.

Since, 1 x 1 = 1

         2 x 2 = 4

         3 x 3 = 9

         4 x 4 = 16

         5 x 5 = 25

         6 x 6 = 36

         7 x 7 = 49

Thus, 36 is a perfact square number between 30 and 40.

√0.053361
= √(5.3361 × 10^(-2))
= √(5.3361) × √(10^(-2))
= ±2.31 × 0.1
= ±0.231

12² = 12*12 = 144

13² = 13*13 = 169

Now numbers are between144 and 169 are:

145, 146, 147,.............168

Total number = 24

So total numbers lies between 144 and 169 is 24

When squaring the number 5278, the unit digit is determined by the square of the unit digit of the original number.

Since the unit digit of 5278 is 8, squaring it gives 8 × 8 = 64.

Therefore, the unit place digit of 5278² is 4.
Therefore correct answer : Option A