Is 2437 is a perfect cube?

Solution:

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• Three number are in the ratio 1 : 2 : 3 and the sum of their cubes is 4500. Find the numbers.
• Important Questions on Cubes and Cube Roots
• Important Points to Remember on Cubes and Cube Roots
• 3D Learning Videos on Related Topics
• Number Patterns From Triangles to Squares
• Prime Factors of a Cube Number
• Cube Root of Numbers by Prime Factorisation Method
• Enrich your Learning with Real Life Examples and DIY Videos
• Euclid's Big Problem
• How to Calculate Cube Roots in Your Head
• Know About Fibonacci Series
• How do you find the smallest number to be divided to get a perfect cube?
• Is 2888 a perfect cube if not find the smallest number that must be a multiplied to get a perfect cube and B to divide to get a perfect cube?
• Is 6000 a perfect cube if not then by which smallest natural number?
• Is 2437 is a perfect cube?

(i) 243

Prime factors of 243 =

Here 3 do not appear in 3’s group.

Therefore, 243 must be multiplied by 3 to make it a perfect cube.

(ii) 256

Prime factors of 256 = 2\times2\times2\times2\times2\times2\times2\times2

Here one factor 2 is required to make a 3’s group.

Therefore, 256 must be multiplied by 2 to make it a perfect cube.

(iii) 72

Prime factors of 72 = 2\times2\times2\times3\times3

Here 3 does not appear in 3’s group.

Therefore, 72 must be multiplied by 3 to make it a perfect cube.

(iv) 675

Prime factors of 675 = 3\times3\times3\times5\times5

Here factor 5 does not appear in 3’s group.

Therefore 675 must be multiplied by 3 to make it a perfect cube.

(v) 100

Prime factors of 100 = 2\times2\times5\times5

Here factor 2 and 5 both do not appear in 3’s group.

Therefore 100 must be multiplied by 2\times5= 10 to make it a perfect cube.

NCERT Practice Workbook Mathematics > Cubes and Cube Roots > SUMMATIVE ASSESSMENT > BASED ON COMPLETE CHAPTER ..... > Q 5

Three number are in the ratio 1 : 2 : 3 and the sum of their cubes is 4500. Find the numbers.

Let the three numbers be y,  2y, 3y.

Given that the sum of cubes of these number is 4500.

Therefore,

⇒y3+2y3+3y3 =4500

⇒y3+8y3+27y3=4500

⇒y3=450036

⇒y3=125

⇒y=1253=5

Therefore, y=5, 2y=10, 3y=15

Hence, the numbers are  5, 10, 15.

Important Questions on Cubes and Cube Roots

NCERT Practice Workbook Mathematics > Cubes and Cube Roots > Worksheet 1 > Q 6

Is 2376 a perfect cube? If not, then by which smallest natural number should 2376 be divided, so that the quotient is a perfect cube?

NCERT Practice Workbook Mathematics > Cubes and Cube Roots > Worksheet 1 > Q 6

Using prime factorization, find if 128 is a perfect cube.

NCERT Practice Workbook Mathematics > Cubes and Cube Roots > Worksheet 2 > Q 2

Find the correct values and complete the table for 857375.

Important Points to Remember on Cubes and Cube Roots

1. Cube of a Number:

(i) The cube of a number is that number raised to the power 3. Thus, if a is a number, then a3=a×a×a.

(ii) A natural number is a perfect cube, if it is cube of some natural number. Thus, a natural number n is a perfect cube. If n=m3 for some natural number m.

2. Properties of Cubes:

(i) The cube of an even natural number is even.

(ii) The cube of an odd natural number is odd.

3. Cube Root:

A number m is the cube root of a natural number n=m3. In other words, a cube root of a number n is the number whose cube is n. The cube root of n is denoted by n3

4. Properties of Cube Roots:

(i)  -n3=-n3

(ii) ab3=a3×b3

(iii) ab3=a3b3, b≠0

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Prime Factors of a Cube Number

The ages of four kids are prime numbers. If the product of their ages is 210, then how can we find their separate ages? Let's understand through this video.

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Finding cube root can involve complex calculation, but not if you know some of the easy tricks. Watch this video to learn one such method.

Enrich your Learning with Real Life Examples and DIY Videos

Euclid's Big Problem

Calculating cube roots was a big problem for Euclid and his cohorts. They thought long and hard to find a solution. Watch this video to know the whole story.

How to Calculate Cube Roots in Your Head

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Know About Fibonacci Series

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How do you find the smallest number to be divided to get a perfect cube?

Prime factorising 81, we get,.

We know, a perfect cube has multiples of 3 as powers of prime factors..

Here, number of 3's is 4..

So we need to divide the factorization by 3 to make 81 a perfect cube..

Hence, the smallest number by which 81 must be divided to obtain a perfect cube is 3..

Is 2888 a perfect cube if not find the smallest number that must be a multiplied to get a perfect cube and B to divide to get a perfect cube?

We observe that if 288 is multiplied by (2 x 3), then its prime factors will exist in triples. Thus, the required smallest number by which 288 be multiplied to make it a perfect cube i: (2 x 3), i.e. 6.

Is 6000 a perfect cube if not then by which smallest natural number?

60006=1000 which is a perfect cube.

Is 2437 is a perfect cube?

(iv) 2437 = 2437 × 1 So, it is not a perfect cube.

What are the perfect cubes 1 to 300?

Is 243a perfect cube?

Is 133100 is a perfect cube?

How do I know a number is a perfect cube?