❤️️ What is the smallest number by which 8640 must be divided so that the quotient is a perfect square? 2022

Contents

1 Mẹo về What is the smallest number by which 8640 must be divided so that the quotient is a perfect square? Mới Nhất
- - 1.0.1 Solution
  - 1.0.2 APPEARS IN
2 What is the smallest number by which 8640 must be divided so that the quotient is a perfect cube?
3 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.

Mẹo về What is the smallest number by which 8640 must be divided so that the quotient is a perfect square? Mới Nhất

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Sum

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

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

Q.
10Q
9Q 11

APPEARS IN

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

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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