Test: A Square and A Cube - 2 - Class 8 MCQ

True
If a³ is the cube and m is one of the prime factors of a. Then, m appears three times in a³.

As 100³ = 1000000 which is the smallest 3 digit number. So it’s only 2 digit number which is the cube root of a 6 digit number

for example like 343 so its cube root will be 7
because 7³ will always have 3 as unit digit

 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)

To find the cube root of 800, we first need to understand what a cube root is. The cube root of a number is a value that, when multiplied by itself three times, gives the original number.

Now, let's break down the number 800 into its prime factors:

• 800 can be factored as 8 × 100.
• Further breaking it down, 8 is 2³ and 100 is 10 × 10, which is 2² × 5².
• So, 800 = 2³ × (2² × 5²) = 2⁵ × 5².

When we take the cube root, we divide the powers by 3:

• The cube root of 2⁵ is 2^1.67 (approximately).
• The cube root of 5² is 5^0.67 (approximately).

After calculating the cube root, we find that 800 does not have any complete sets of three in its prime factorisation. Therefore, it does not produce a whole number.

Thus, the number of zeros in the cube root of 800 is 0.

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.

To find the cube root of 512, we recognise that:

• 8³ = 512

Therefore, the cube root of 512 can be expressed as:

• √₃(512) = 8

The cube of 4 is:

The answer is 1681 because it is the only number which has it's last digit as a number which a perfect square can have . 9×9=81 the last digit is 1.

Option B is correct because the unit digit of 161 is 1 and if unit digit of any digit ends with 1 the its square will also end with 1.

We are told that the sum of squares of two numbers is 145 and the square root of one number is 3.

Step 1: If the square root of a number is 3, then the number is 3 × 3 = 9.

Step 2: Let the other number be x. According to the question,
(square of first number) + (square of second number) = 145
9 × 9 + x × x = 145
81 + x² = 145

Step 3: Subtract 81 from 145.
x² = 145 – 81 = 64

Step 4: Take the square root.
x = 8

Final Answer: The other number is 8 (option b).

√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