CBSE Class 8 Maths Cubes and Cube Roots Worksheet Set 01

Very Short Answer type Questions

Question. If square of a number having digit 9 at unit’s place then what will be the digit at unit’s place in the cube of that numbers?
Answer : 7 or 3.

Question. (3√729)³ = __________ complete it.
Answer : 729

Question. Simplify : 3√1.1 3 x 3√1.331)
Answer : 1.21

Question. What is the volume of a cube if the area of one face is 36 cm²?
Answer : 216 cm³

Question. Which least number should be multiplied by 2 × 2 × 7 × 7 × 5 × 7 × 5 × 5 to get a perfect cube?
Answer : 2

Question. Simplify : 15³ – 14³.
Answer : 631

Question. What is 11³ – 10³?
Answer : 331

Question. Complete it 3√825 > _____ . (whole number).
Answer : 9

Question. What is x if 3^x = 243.
Answer : 5

Question. What is cube of 8/11 ?
Answer : 512/1331

Question. By which least number 250 × 512 should be divided to make it a perfect cube.
Answer : 2

Question. What is 10³ – 9³?
Answer : 271

Question. By which least no 1024 should be divided to make it a perfect cube.
Answer : 2

Question. Find √0.001/1.331 and give the answer.
Answer : 1/11

LOB: Define perfect cube/cube number in order to classify the given numbers as cube numbers or non-cube numbers

Question. Is 343 a perfect cube?
Option 1: Yes, because 3 is in one’s place.
Option 2: No, because it is an odd number.
Option 3: No, because the sum of the digits is not a perfect cube.
Option 4: Yes, because all its prime factors can be grouped in triples.
Answer : Option 4

Question. Consider the given set of numbers.
{215, 625, 841, 1000, 1331, 2744, 12321, 27000, 35937, 64000}
Which option correctly classifies the given numbers as cube numbers and non-cube numbers?
Option 1: There are 6 cube numbers and 4 non-cube numbers in the given set.
Option 2: There are 5 cube numbers and 5 non-cube numbers in the given set.
Option 3: There are 4 cube numbers and 6 non-cube numbers in the given set.
Option 4: There are 3 cube numbers and 7 non-cube numbers in the given set.
Answer : Option 1

LOB: Observe the pattern of cube of even numbers in order to generalize that cubes of even numbers are even

Question. Observe the pattern shown below.
8, 64, 216, 512, …
Based on the pattern, which statement is true?
Option 1: Cubes of all odd numbers are odd.
Option 2: Cubes of all even numbers are even.
Option 3: Cubes of all odd numbers end only in 1, 3, 5 and 7.
Option 4: Cubes of all even numbers end only in 2, 4, 6 and 8.
Answer : Option 2

Question. If c is an even number, which statement is correct about the value of the expression [c + (c + 2) + (c + 4) + (c + 6) + …]3?
Option 1: For any value of c, the value of the expression will be an odd number.
Option 2: For any value of c, the value of the expression will be a prime number.
Option 3: For any value of c, the value of the expression will be an even number.
Option 4: For any value of c, the value of the expression will be an irrational number.
Answer : Option 3

LOB: Observe the pattern of cube of numbers with one's digit as 1, 2, 3, 4, etc. in order to explore the one's digit of their perfect cubes and comment on it

Question. Which digit comes in one’s place in the cube of 17325483?
Option 1: 1
Option 2: 3
Option 3: 7
Option 4: 9
Answer : Option 3

Question. Which digit comes in one’s place in the result of the expression (21476 + 31520 + 41305 + 50697)3?
Option 1: 2 because 6 + 0 + 5 + 7 = 18 and 8 × 8 × 8 = 512
Option 2: 2 because 2 + 3 + 4 + 5 = 14 and 4 + 4 + 4 = 12
Option 3: 4 because 2 + 3 + 4 + 5 = 14 and 4 × 4 × 4 = 64
Option 4: 4 because 6 + 0 + 5 + 7 = 18 and 8 + 8 + 8 = 24
Answer : Option 1

LOB: Add n consecutive odd numbers in order to get the sum equal to n³

Question. How many consecutive odd numbers must be added to get the sum equal to 243?
Option 1: 2
Option 2: 4
Option 3: 20
Option 4: 24
Answer : Option 4

Question. Which of the following expressions can be used to find the value of [(43 + 45 + 47 + 49 + 51 + 53 + 55) – (31 + 33 + 35 + 37 + 39 + 41)]?
Option 1: 1 × 6 × 5 + 3
Option 2: 1 × 6 × 5 × 3
Option 3: 1 × 7 × 6 + 3
Option 4: 1 × 7 × 6 × 3
Answer : Option 4

LOB: Use prime factorization in order to rule out a number as a perfect cube

Question. Which of the following expressions will not yield a perfect cube?
Option 1: 2 × 2 × 2 × 3 × 3 × 3
Option 2: 4 × 4 × 4 × 4 × 4 × 4 × 5 × 5 × 5
Option 3: 6 × 6 × 6 × 6 × 6 × 6 × 3 × 3 × 3 × 3
Option 4: 8 × 8 × 8 × 4 × 4 × 4 × 5 × 5 × 5 × 5 × 5 × 5
Answer : Option 3

Question. Nimish claims that –1728 is not a perfect cube number. Which of the following options justifies his claim?
Option 1: Nimish’s claim is incorrect because each prime factor of –1728 appears three times.
Option 2: Nimish’s claim is correct because 8 is in one’s place which is not divisible by 3.
Option 3: Nimish’s claim is incorrect because 1 + 7 + 2 + 8 = 18 which is divisible by 3.
Option 4: Nimish’s claim is correct because –1728 is a negative integer.
Answer : Option 1

LOB: Use prime factorization on the given number in order to find the smallest number to be operated (all the four arithmetic operations) on given number to get a perfect cube

Question. Which smallest number should be multiplied to 2592 so that the product is a perfect cube?
Option 1: 2
Option 2: 3
Option 3: 12
Option 4: 18
Answer : Option 4

Question. If k = (m × n)4 where m and n are the prime factors of k, which expression will result in a perfect cube nearest to k with only factors m and n?
Option 1: k ÷ (m × n)
Option 2: k + (m × n)
Option 3: k × (m × n)²
Option 4: k – (m × n)²
Answer : Option 1

LOB: Use prime factorization in order to find the cube root of a given number

Question. Which of the following options correctly shows the cube root of 13824?
Option 1: 13824 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 = 2 × 2 × 2 × 2 × 6 × 9 = 864
Option 2: 13824 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 = 2 + 2 + 2 + 2 + 6 + 9 = 23
Option 3: 13824 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 = 2 × 2 × 2 × 3 = 24
Option 4: 13824 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 = 2 + 2 + 2 + 3 = 9
Answer : Option 3

Question. If s and m are two perfect cube numbers such that s = (a × b)6 and 𝑚 = B * , which expression can be used to represent the cube root of m?
Option 1: ab/2
Option 2: ab/4
Option 3: (ab)²/2
Option 4: (ab)²/4
Answer : Option 3

LOB: Use estimation in order to find the cube root of a given perfect cube

Question. What is the estimated cube root of 50653?
Option 1: 37
Option 2: 50
Option 3: 53
Option 4: 65
Answer : Option 1

Question. What is the cube root of 857375?
Option 1: Cube root of 857375 is 85 because 8 is the leftmost digit and 5 is the rightmost digit in 857375.
Option 2: Cube root of 857375 is 98 because 8 is the greatest digit in 857375 and 93 < 857 < 103.
Option 3: Cube root of 857375 is 95 because 5 is the unit digit in 857375 and 93 < 857 < 103.
Option 4: Cube root of 857375 is 75 because both 5 and 7 are repeated in 857375.
Answer : Option 3