find the smallest number by which 4860 should be multiplied so that the product is a perfect cube pleaseeeeeee answer asap
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Subject:
Math -
Author:
leslybarton -
Created:
1 year ago
Answers 2
The smallest number is 150, which when multiply by 4860; becomes a perfect cube.
Step-by-step explanation:
Given:
- 4860
To find:
- Find the smallest number by which 4860 should be multiplied so that the product is a perfect cube.
Solution:
Concept to be used:
- Prime factorise the number.
- Make pairs of 3-3 same prime numbers; because [tex]\bf \sqrt[3]{ {a}^{3} } = a[/tex]
Step 1:
Write prime factors of 4860.
[tex]4860 = 2 \times 2 \times 3 \times 3 \times 3 \times 3 \times 3 \times 5 \\ [/tex]
or
[tex]4860 =( 2 \times 2) \times (3 \times 3 \times 3) \times (3 \times 3 )\times (5 )\\ [/tex].
Step 2:
Complete the triplets.
In first bracket; multiply 2,to complete the triplet.
Second triplet is complete.
In third bracket, multiply 3, to complete the triplet.
In fourth bracket, multiply 25, to complete the triplet.
So,
[tex]2 \times 3 \times 25 = 150 \\ [/tex]
If we multiply 150 to 4860, it will become 729000; which is a perfect cube of 90.
Thus,
The smallest number is 150, which when multiply by 4860; becomes a perfect cube.
Learn more:
1) find the smallest number by 13720 must be multiplied to obtain a perfect cube
https://brainly.in/question/3593344
2) The smallest number by which 1944 should be multiplied so that it becomes a
perfect cube is-
(i)3
(ii) 2
(iii)5
https://brainly.in/question/17167808
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Author:
alejogonzalez
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Rate an answer:
1
To find the smallest number by which 4860 should be multiplied so that the product is a perfect cube.
we have to use the method of prime factorization,
4860 can be expressed as:
4860 = 2 × 2 × 3 × 3 × 3 × 3 × 3 × 5
= ( 2×2 ) × (3×3×3 ) × ( 3 ×3 ) × 5
Here to complete the triplet of [( 2 × 2), ( 3 × 3 )and 5] we need to multiply:-
[( 2×2 )×2=2³
( 3× 3)×3² = 3³
(5 ) ×5×5= 5×5²=5³]
2× 3 × 5×5
= 2×3 × 5²
= 150
∴We need to multiply 4860 by (2 × 3 × 5 × 5) 150.
⇒ 4860 × 150 = 729000 ( 729000m is the perfect cube of 90 )
Hence, the smallest number by which 4860 should be multiplied so that the product is a perfect cube is 150.
Ans :- The smallest number by which 4860 should be multiplied so that the product is a perfect cube is 150.
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