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Nội dung chính

  • What is the smallest number by which 8640 must be divided so that the quotient is a perfect cube?
  • The correct option is C 5 336453121534053135345315551Using prime factorization method we have, 3645=3×3×3×3×3×3×5Grouping in pairs we get (3×3)×(3×3)×(3×3)×5 ∴ We have to multiply 3645 by 5 to get a
    perfect square.
  • What is the smallest number that should divide 3645 to get a perfect cube?
  • Is 3645 a perfect cube?
  • Is 3645 a perfect square?
  • What should be divided from 3645 to get a perfect square?
  • What is the smallest number by which 8640 must be divided to make it a perfect square?
  • What is the perfect cube of 8640?
  • Which smallest number should 42592 be divided so that the quotient is a perfect cube?
  • What is least number by which 13720 must be divided so the quotient is a perfect cube?
  • What least number Must 8640 be divided so that the quotient is a perfect square?
  • What is the perfect cube of 8640?
  • What is least number by which 13720 must be divided so the quotient is a perfect cube?
  • What is the smallest number by which 5184 must be divided so that the quotient is a perfect cube also find the cube root of the quotient so obtained?

With what least number must 8640 be divided so that the quotient is a perfect cube?

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Solution

The prime factors of 8640 are

2
8640
2
4320
2
2160
2
540
2
270
3
135
3
45
3
15
5
5
 
1

= 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 5
= (2 x 2 x 2) x (2 x 2 x 2) x (3 x 3 x 3) x 5
Clearly, 8640 must be divided by 5.

Concept: Cube Root Through Prime Factorisation Method

  Is there an error in this question or solution?

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Chapter 4: Cubes and Cube Roots – Exercise 4 (A) [Page 48]

Q.
10Q
9Q 11

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Selina Concise Mathematics Class 8 ICSE

Chapter 4 Cubes and Cube Roots
Exercise 4 (A) | Q. 10 | Page 48

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Nội dung chính

Nội dung chính

  • What is the smallest number by which 8640 must be divided so that the quotient is a perfect cube?
  • The correct option is C 5 336453121534053135345315551Using prime
    factorization method we have, 3645=3×3×3×3×3×3×5Grouping in pairs we get (3×3)×(3×3)×(3×3)×5 ∴ We have to multiply 3645 by 5 to get a perfect square.
  • What is the smallest number that should divide 3645 to get a perfect cube?
  • Is 3645 a perfect cube?
  • Is 3645 a perfect square?
  • What should be divided from 3645 to get a perfect square?
  • Related Videos
  • What is the smallest number by which 8640 must be divided to make it a perfect square?
  • What is the perfect cube of 8640?
  • Which smallest number should 42592 be divided so that
    the quotient is a perfect cube?
  • What is least number by which 13720 must be divided so the quotient is a perfect cube?
  • What is the smallest number by which 8640 must be divided so that the quotient is a perfect cube?
  • The
    correct option is C 5 336453121534053135345315551Using prime factorization method we have, 3645=3×3×3×3×3×3×5Grouping in pairs we get (3×3)×(3×3)×(3×3)×5 ∴ We have to multiply 3645 by 5 to get a perfect square.
  • What is the smallest number that should divide 3645 to get a perfect cube?
  • Is 3645 a perfect cube?
  • Is 3645 a perfect square?
  • What should be divided from 3645 to get a perfect square?

What is the smallest number by which 8640 must be divided so that the quotient is a perfect cube?

Answer

Verified

Hint: This question can be done easily by prime factorization method
In order to find the smallest number to be divided first we
factorize 8640.
$
   Rightarrow 8640 = 2 times 2 times 2 times 2 times 2 times 2 times 3 times 3 times 3 times 5 \
Rightarrow 8640 = 2^6 times 3^3 times 5 \ $
In the above factorization, we find that there is a triplet of 2 and 3 but there is no triplet of 5.
Hence, 5 is the smallest number which must divide 8640 so that the quotient is a perfect cube.

Note: Any number which is a perfect cube will be multiple of a triplet of digits. Cube
roots of the number can also be found out by the above mentioned prime factorization method.

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Solution

The correct option is C 5 336453121534053135345315551Using prime factorization method we have, 3645=3×3×3×3×3×3×5Grouping in pairs we get (3×3)×(3×3)×(3×3)×5 ∴ We have to multiply 3645 by 5 to get a
perfect square.

TextbooksQuestion PapersHome

What is the smallest number that should divide 3645 to get a perfect cube?

Hence the smallest number by which 3645 must be multiplied to get a perfect cube is 25.

Is 3645 a perfect cube?

If we look the number 3645, we know that the cube root is 15.38978352009, and
since this is not a whole number, we also know that 3645 is not a perfect cube.

Is 3645 a perfect square?

Answer. 3645 is not a perfect square.

What should be divided from 3645 to get a perfect square?

Therefore, The required smallest number by which 3645 must be multiplied to get a perfect square is 5.

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What is the smallest number by which 8640 must be divided to make it a perfect square?

Hence, 5 is the smallest number by which 8640 must be divided, so that the quotient is a perfect cube. Was this answer helpful?

What is the perfect cube of 8640?

8640 is not a perfect cube.

Which smallest number should 42592 be divided so that the quotient is a perfect cube?

Answer: 4 is the smallest number should 42592 be divided so that the quotient is a perfect cube.

What is least number by which 13720 must be divided so the quotient is a perfect cube?

Now it gives
the value $ 2^3 times 7^3 = 2744 $ . Hence $ 5 $ is the least number by which $ 13720 $ must be divided so that the quotient is a perfect cube. So, the correct answer is “5”.

What least number Must 8640 be divided so that the quotient is a perfect square?

Solution. Clearly, 8640 must be divided by 5.

What is the perfect cube of 8640?

8640 is not a perfect cube.

What is least number by which 13720 must be divided so the quotient is a perfect cube?

Now it gives the value $ 2^3 times 7^3 = 2744 $ . Hence $ 5 $ is the least number by which $ 13720 $ must be divided so that the quotient is a perfect cube. So, the correct answer is “5”.

What is the smallest number by which 5184 must be divided so that the quotient is a perfect cube also find the cube root of the quotient so obtained?

We find that in 5184 one ‘3’ is ungrouped. Thus, to convert 5184 to a perfect cube, we need to multiply it by 3×3=9.
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