What Is The Cube Root Of 1000? - [Explanation] Culture of the whole world

10 The cube root of 1000 is 10. A real cube root of the given equation is 10.

What is 1000000000 ka cube root?

Answer. The cube root of 1000000000 is 1000.

Why is 1000 not a perfect cube?

(i) 216
(ii) 128
(iii) 1000
(iv) 100
(v) 46656
Sol. (i) We have 216 = 2 × 2 × 2 × 3 × 3 × 3
Grouping the prime factors of 216 into triples, no factor is left over.
∴ 216 is a perfect cube.

(ii) We have 128 = 2 × 2 × 2 × 2 × 2 × 2 × 2
Grouping the prime factors of 128 into triples, we are left over with 2 as ungrouped factor.
∴ 128 is not a perfect cube.

(iii) We have 1000 = 2 × 2 × 2 × 5 × 5 × 5
Grouping the prime factors of 1000 into triples, we are not left over with any factor.
∴ 1000 is a perfect cube.

(iv) We have 100 = 2 × 2 × 5 × 5 Grouping the prime factors into triples, we do not get any triples. Factors 2 × 2 and 5 × 5 are not in triples. ∴ 100 is not a perfect cube.

(v) We have 46656 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 × 3 × 3 × 3
Grouping the prime factors of 46656 in triples we are not left over with any prime factor.
∴ 46656 is a perfect cube.

Q2. Find the smallest number by which each of the following numbers must be multiplied to obtain a perfect cube.

(i) 243
(ii) 256
(iii) 72
(iv) 675
(v) 100
Sol. (i) We have 243 = 3 × 3 × 3 × 3 × 3

The prime factor 3 is not a group of three.
∴ 243 is not a perfect cube.
Now, × 3 = × 3
or 729 =3 × 3 × 3 × 3 × 3 × 3
Now, 729 becomes a perfect cube.
Thus, the smallest required number to multiply 243 to make it a perfect cube is 3.

(ii) We have 256 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2

Grouping the prime factors of 256 in triples, we are left over with 2 × 2.
∴ 256 is not a perfect cube.
Now, × 2 = × 2
or 512 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2

i.e.512 is a perfect cube. Thus, the required smallest number is 2. (iii) We have 72 = 2 × 2 × 2 × 3 × 3

Grouping the prime factors of 72 in triples, we are left over with 3 × 3.
∴ 72 is not a perfect cube.
Now, × 3 = × 3
or 216 = 2 × 2 × 2 × 3 × 3 × 3

i.e.216 is a perfect cube. ∴ The smallest number required to multiply 72 to make it a perfect cube is 3. (iv) We have 675 = 3 × 3 × 3 × 5 × 5

Grouping the prime factors of 675 to triples, we are left over with 5 × 5.
∴ 675 is not a perfect cube.
Now, × 5 = × 5
or 3375 = 3 × 3 × 3 × 5 × 5 × 5
Now, 3375 is a perfect cube.
Thus, the smallest required number to multiply 675 such that the new number perfect cube is 5.
(v) We have 100 = 2 × 2 × 5 × 5

The prime factor are not in the groups of triples.
∴100 is not a perfect cube.
Now × 2 × 5 = × 2 × 5
or × 10 = 2 × 2 × 2 × 5 × 5 × 5
1000 = 2 × 2 × 2 × 5 × 5 × 5
Now, 1000 is a perfect cube.
Thus, the required smallest number is 10.

Q3. Find the smallest number by which each of the following numbers must be divided to obtain a perfect cube.

(i) 81
(ii) 128
(iii) 135
(iv) 192
(v) 704
Sol. (i) We have 81 = 3 × 3 × 3 × 3

Grouping the prime factors of 81 into triples, we are left with 3.
∴ 81 is not a perfect cube.
Now, 3 = + 3
or 27 = 3 × 3 × 3

i.e.27 is a prefect cube Thus, the required smallest number is 3. (ii) We have 128 = 2 × 2 × 2 × 2 × 2 × 2 × 2

Grouping the prime factors of 128 into triples, we are left with 2.
∴ 128 is not a perfect cube
Now, 2 = 5 = 5
or 27 = 3 × 3 × 3

i.e.27 is a perfect cube. Thus, the required smallest number is 5. (iv) We have 192 = 2 × 2 × 2 × 2 × 2 × 2 × 3

Grouping the prime factors of 192 into triples, 3 is left over.
∴ 192 is not a perfect cube.
Now, 3 = 11 = × 5 cm × 2 cm × 2 cm
= = 20 cm3
Thus, the required number of cuboids = 20.

1. Find the cube root of each of the following numbers by prime factorisation method.

(i) 64
(ii) 512
(iii) 10648
(iv) 27000
(v) 15625
(vi) 13824
(vii) 110592
(viii) 46656
(ix) 175616
(x) 91125

Sol. (i) By prime factorisation, we have (ii) By prime factorisation, we have (iii) By prime factorisation, we have Thus, cube root of 10648 is 22. (iv) By prime factorisation, we have Thus, cube root of 27000 is 30. (v) By prime factorisation, we have Thus, cube root of 15625 is 25. (vi) By prime factorisation, we have Thus, cube root of 13824 is 24. (vii) By prime factorisation, we have Thus, the cube root of 110592 is 48 (viii) By the prime factorisation, we have Thus, the cube root of 46656 is 32 (ix) By prime factorisation, we have

175616 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 7 × 7 × 7
= 2 × 2 × 2 × 7 = 56
Thus the cube root of 175616 is 56.
(x) By prime factorisation, we have:

91125 = 3 × 3 × 3 × 3 × 3 × 3 × 5 × 5 × 5
= 3 × 3 × 5 = 45
Thus, the cube root of 91125 is 45.

Q2. State true or false.

(i) Cube of any odd number is even.
(ii) A perfect cube does not end with two zeros.
(iii) If square of a number ends with 5, then its cube ends with 25.
(iv) There is no perfect cube which ends with 8.
(v) The cube of a two digit number may he a three digit number.
(vi) The cube of a two digit number may have seven or more digits.
(vii) The cube of a single digit number may be a single digit number.
Sol. (i) False (ii) True (iii) False (iv) False
(v) False (vi) False (vii) True

Q3. You are told that 1,331 is a perfect cube. Can you guess without factorisation what is its cube root? Similarly, guess the cube roots of 4913, 12167, 32768.

Sol. (i) Separating the given number (1331) into two groups:
1331 → 1 and 331
∴ 331 end in 1.
∴ Unit’s digit of the cube root = 1

∴ Ten’s digit of the cube root = I

(ii) Separating the given number (4913) in two groups:
4913 → 4 and 913
Unit’s digits:
∵ Unit’s digit in 913 is 3.
∴ Unit’s digit of the cube root = 7
Ten’s digit:
1 3 = 1, 2 3 = 8
and 1 < 4 < 8

i.e.13 < 4 < 23 ∴ The ten's digit of the cube root is 1.

(iii) Separating 12,167 in two groups:
12167 → 12 and 167
Unit’s digit:
∵ 167 is ending in 7 and cube of a number ending in 3 ends in 7.
∴ The unit’s digit of the cube root = 3
Ten’s digit:
∵ 2 3 = 8 and 3 3 = 27
Also, 8 < 12 < 27
or 23 < 12 < 32
∴ The tens digit of the cube root can be 2.

(iv) Separating 32768 in two groups:
32768 → 32 and 786
Unit’s digit:
768 will guess the unit’s digit in the cube root.
∵ 768 ends in 8.
Unit’s digit in the cube root = 2
Ten’s digit:
∵ 3 3 = 27 and 4 3 – 64
Also, 27 < 32 < 64
or 33 < 32 < 43
The ten’s digit of the cube root = 3.

: CBSE 8, Math, CBSE- Cubes and Cube Roots, NCERT Solutions

When cubed is 1000?

The cube of 1000 is 1000 × 1000 × 1000 = 1,000,000,000.

What is the value of ∛ 1404928?

Therefore, cube root of 1404928=2×2×2×2×7=16×7= 112. Therefore, the cube root of 1404928 is 112.

Is 8 000 a perfect cube?

As the cube root of 8000 is a whole number, 8000 is a perfect cube.

Is 49 a perfect square?

Informally: When you multiply an integer (a “whole” number, positive, negative or zero) times itself, the resulting product is called a square number, or a perfect square or simply “a square.” So, 0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, and so on, are all square numbers. More formally: A square number is a number of the form n × n or n 2 where n is any integer.

Is 1000000000000 a perfect cube?

1000000000 is said to be a perfect cube because 1000 x 1000 x 1000 is equal to 1000000000. Since 1000000000 is a whole number, it is a perfect cube. The nearest previous perfect cube is 997002999.

Cube Root Chart Perfect Cube Of Numbers

Cube Root of 1000000000

∛1000000000 = ∛(1000 x 1000 x 1000) 1000

ul> Perfect ∛997002999

1000000000 is said to be a perfect cube because 1000 x 1000 x 1000 is equal to 1000000000. Since 1000000000 is a whole number, it is a perfect cube. The nearest previous perfect cube is 997002999.

Is 1000000 a perfect cube True or false?

State True Or False. a Perfect Cube Does Not End with Two Zeroes. – Mathematics | Shaalaa.com State true or false. A perfect cube does not end with two zeroes. For finding the cube of any number, the number is first multiplied with itself and this product is again multiplied with this number.

How do you find the perfect cube of 1000?

A perfect cube is a number which is the cube of an integer. Since the cube of 10 is 1000, 1000 is a perfect cube number.

Is 0 a cube number?

What are the First 11 Cube Numbers? – The first 11 cube numbers are 0, 1, 8, 27, 64, 125, 216, 343, 512, 729, and 1000.

How many cubes in 1000?

There are 8 perfect cubes between 1 and 1000. Was this answer helpful?

What is the square root of 65536?

Therefore, \sqrt = 256.

What is the square number of 20164?

∴ The square root of 20164 is 142, i.e. √20164 = 142.

What is the total value of 2 in 12678?

Hence, in the give number 12678, digit 2 represents 2 thousands or 2000. The value of 2 in 12678 is actually referring the place value of 2 which is 2000.

Is 10000000 a perfect cube?

1000000 is said to be a perfect cube because 100 x 100 x 100 is equal to 1000000. Since 1000000 is a whole number, it is a perfect cube. The nearest previous perfect cube is 970299 and the nearest next perfect cube is 1030301,

Cube Root Chart Perfect Cube Of Numbers

Cube Root of 1000000

∛1000000 = ∛(100 x 100 x 100) 100

ul> Perfect ∛970299 Perfect ∛1030301

Is 2025 a perfect cube?

Yes, because ∛2025 = ∛(3 × 3 × 3 × 3 × 5 × 5) = 3 ∛75 and it cannot be expressed in the form of p/q where q ≠ 0.

Is 13824 a perfect cube?

Show that each of the following numbers is a perfect cube Also find the number whose cube is the giv. Question 2 Cubes and Cube Roots Exercise 4.1 Answer: (i) We have, 1728 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3

After grouping the prime factors in triplets, it’s seen that no factor is left without grouping.
1728 = (2 × 2 × 2) × (2 × 2 × 2) × (3 × 3 × 3)
Thus, 1728 is a perfect cube and its cube root is 2 × 2 × 3 = 12.
(ii) We have,

After grouping the prime factors in triplets, it’s seen that no factor is left without grouping.
5832 = (2 × 2 × 2) × (3 × 3 × 3) × (3 × 3 × 3)
Thus, 5832 is a perfect cube and its cube root is 2 × 3 × 3 = 18
(iii) We have,
13824 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3

After grouping the prime factors in triplets, its seen that no factor is left without grouping.
13824 = (2 × 2 × 2) × (2 × 2 × 2) × (2 × 2 × 2) × (3 × 3 × 3)
Thus, 13824 is a perfect cube and its cube root is 2 × 2 × 2 × 3 = 24.
(iv) We have,

Was This helpful? : Show that each of the following numbers is a perfect cube Also find the number whose cube is the giv.

Is 1000000000 a perfect cube?

1000000000 is said to be a perfect cube because 1000 x 1000 x 1000 is equal to 1000000000. Since 1000000000 is a whole number, it is a perfect cube.

What is root 3 1000000?

The cube root of 1000000 = 100.

What is 2100 ka under root?

The square root of 2100 is 45.82575.

How many zeros are there in cube root of 1000000?

Answer: The number of zeroes at the end of the cube root of the number 1000000 is 2.