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Question

The difference between the square root and the cube root of the number \(729 \times 64\) is:

This question was previously asked in
CTET 2022 Paper 2 Maths Question Paper (Jan-27-2023) (Eng-Hin-Skt)
The correct answer is

180

The number is \(729 \times 64\), and since \(729 = 27^2\) and \(64 = 8^2\), the square root is \(27 \times 8 = 216\).

Also, since \(729 = 9^3\) and \(64 = 4^3\), the cube root is \(9 \times 4 = 36\).

The difference between the square root and the cube root is \(216 - 36 = 180\).

Hence, the difference is \(180\).

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Important Questions from Square and Square Root

  1. The sum of the squares of two positive integers is 306. If the square of the larger integer is 25 times the smaller integer, then the difference between the two integers is

  2. \(\sqrt{625.0025 }=\)
  3. The least number which is a perfect square and is divisible by each of the numbers 4, 10 and 12 is :

  4. The addition of the squares of two numbers in squares is 221. What are those numbers?

  5. Find the value of \(\sqrt{9604} \).

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