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Class 10MathematicsReal NumbersFundamental Theorem of ArithmeticExpertLevel 5
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What is the smallest positive number by which 21600 must be multiplied to get a perfect square?

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Answer and explanation

Correct answer: 6

Step 1: (21600=216\times100=2^5\times3^3\times5^2). Step 2: For a perfect square, all exponents must be even, but powers of 2 and 3 are odd. Step 3: Multiplying by (2\times3=6) makes all powers even.

Related tags

Perfect-SquarePrime-ExponentsExpert

Frequently asked questions

What is the correct answer to this question?

6

Why is this the correct answer?

Step 1: (21600=216\times100=2^5\times3^3\times5^2). Step 2: For a perfect square, all exponents must be even, but powers of 2 and 3 are odd. Step 3: Multiplying by (2\times3=6) makes all powers even.

Which subject and chapter does this question cover?

This is a Class 10 Mathematics question. Chapter: Real Numbers. Topic: Fundamental Theorem of Arithmetic.

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  1. 1According to the Fundamental Theorem of Arithmetic, every composite number can be written in which form?
  2. 2What is the prime factorisation of 36?
  3. 3What is the correct prime factorisation of 60?
  4. 4What does uniqueness mean in the Fundamental Theorem of Arithmetic?
  5. 5In the prime factorisation of 84, what is the power of 2?
  6. 6The number (2^3\times3^2) is equal to which number?
  7. 7Which is the prime factorisation of 45?
  8. 8Which of the following numbers is prime?
  9. 9Which of the following numbers is composite?
  10. 10What is the prime factorisation of 90?
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