Which of the following is equal to 8³?

• 8 + 8 + 8

• 8 x 3

• 8 x 8 x 8

• 3⁸

Answer explanation

8³ = 8 x 8 x 8

Tags

CCSS.6.EE.A.1

Rahul has a few cubes. The edge length of each cube is 1 cm. He wants to make a bigger cube by arranging the smaller cubes. Which of the following number of cubes he can use to make a bigger cube? 27, 25, 49, 36, 64

• 27 and 64

• 27, 25 and 36

• Only 27

• All of the above

Answer explanation

A bigger cube can be made using smaller cubes only if the number of cubes is a perfect cube. 27 = 3 x 3 x 3 so, a bigger cube can be made using 27 smaller cubes. 64 = 4 x 4 x 4 so, a bigger cube can be made using 64 smaller cubes. It is not possible to make a bigger cube using 25, 49, 36 because these are not perfect cubes. 25 = 5 x 5, 49 = 7 x 7, 36 = 2 x 2 x 3 x 3

Tags

CCSS.8.EE.A.2

Which of the following statements are true? Statement I: The cube of an even number is always even. Statement II: The cube of an odd number is either even or odd.

• Statement I only

• Statement I and II both

• Statement II only

• Neither statement I nor statement II

Answer explanation

Only statement I is true because the cube of an even number is always even. And the cube of an odd number is always odd.

Tags

CCSS.6.EE.B.6

If the units place digit of a number is 7, then the units place digit of its cube is ___

• 7

• 4

• 1

• 3

Answer explanation

If the units place digit of a number is 7, then the units place digit of its cube is 3. E.g. 7³ = 343 e.g. 17³ = 17 x 17 x 17 = 4913

Tags

CCSS.8.EE.A.2

Which of the following is the cube of 248?

• 15252992

• 25252998

• 18252994

• 15252996

Answer explanation

The units place digit of the number 248 is 8 so, its cube must have 2 at its units place. Among given options we see that only 15252992 has 2 at its units place, hence it must be the answer.

Tags

CCSS.8.EE.A.2

Which of the following is a perfect cube?

• 525

• 999

• 343

• 250

Answer explanation

If a number is a perfect cube then each prime factor of the number appears three times in its prime factorisation. 525 = 3 x 5 x 5 x 7 = 3¹ x 5² x 7¹. Here none of the prime factors appear three times, hence 525 is not a perfect cube. 250 = 2 x 5 x 5 x 5 = 2¹ x 5³ since 2 does not appear three times, hence 250 is not a perfect cube. 343 = 7 x 7 x 7 = 7³, here, since the only prime factor 7 of 343 appear 3 times hence this is a perfect cube. 999 = 3 x 3 x 3 x 37 = 3³ x 37¹ since 37 does not appear three times, hence 999 is not a perfect cube.

Tags

CCSS.8.EE.A.2

What is the smallest natural number which must be multiplied with 1800 to obtain a perfect cube?

• 15

• 3

• 5

• 18

Answer explanation

1800 = 2 x 2 x 2 x 3 x 3 x 5 x 5 As we can see, 2 is appearing three times but each of 3 and 5 are appearing only 2 times so to obtain a perfect cube we must multiply both sides by (3 x 5) So, 1800 x (3 x 5) = 2 x 2 x 2 x 3 x 3 x 3 x 5 x 5 x 5 Thus, 1800 x 15 = 27000 which is a perfect cube. So, smallest natural number that must be multiplied with 1800 to obtain a perfect cube is 15.

Tags

CCSS.8.EE.A.2