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Question (1)

QN0029273

A number has the prime factorisation 2⁴ × 3² × 5². Which of the following is true?

(A) It is neither a perfect square nor a perfect cube
(B) It is a perfect square only
(C) It is a perfect cube only
(D) It is both a perfect square and a perfect cube

Correct Answer: B

Explanation:

All prime exponents are even, so the number is a perfect square. Since all exponents are not multiples of 3, it is not a perfect cube.

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Question (2)

QN0029274

Which of the following numbers is both a perfect square and a perfect cube?

(A) 144
(B) 216
(C) 729
(D) 4096

Correct Answer: C

Explanation:

729 = 3⁶ = (3³)² = (3²)³. Hence it is both a perfect square and a perfect cube.

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Question (3)

QN0029275

The least number that must be multiplied by 180 to make it a perfect square is:

(A) 2
(B) 3
(C) 5
(D) 10

Correct Answer: C

Explanation:

180 = 2² × 3² × 5. Multiplying by 5 makes the exponent of 5 even.

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Question (4)

QN0029276

The square root of a number is 18. What is the number?

(A) 324
(B) 288
(C) 196
(D) 648

Correct Answer: A

Explanation:

Number = 18² = 324.

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Question (5)

QN0029277

Which of the following cannot be a perfect square?

(A) 529
(B) 784
(C) 938
(D) 961

Correct Answer: C

Explanation:

A perfect square never ends with 2, 3, 7 or 8. Hence 938 cannot be a perfect square.

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Question (6)

QN0029278

If 49² = 2401, then 50² is:

(A) 2499
(B) 2500
(C) 2501
(D) 2600

Correct Answer: B

Explanation:

50² = (49 + 1)² = 49² + 2×49 + 1 = 2500.

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Question (7)

QN0029279

A square field has an area of 1024 m². Its perimeter is:

(A) 64 m
(B) 96 m
(C) 128 m
(D) 256 m

Correct Answer: C

Explanation:

Side = √1024 = 32 m. Perimeter = 4 × 32 = 128 m.

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Question (8)

QN0029280

Which of the following is a perfect cube?

(A) 972
(B) 1000
(C) 1458
(D) 1728

Correct Answer: D

Explanation:

1728 = 12³.

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Question (9)

QN0029281

The cube root of 2197 is:

(A) 11
(B) 12
(C) 13
(D) 17

Correct Answer: C

Explanation:

13³ = 2197.

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Question (10)

QN0029282

Which number lies exactly halfway between the perfect squares 225 and 289?

(A) 250
(B) 255
(C) 257
(D) 260

Correct Answer: C

Explanation:

(225 + 289) ÷ 2 = 257.

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Question (1)

A number has the prime factorisation 2⁴ × 3² × 5². Which of the following is true?

Explanation:

Link:

Question (2)

Which of the following numbers is both a perfect square and a perfect cube?

Explanation:

Link:

Question (3)

The least number that must be multiplied by 180 to make it a perfect square is:

Explanation:

Link:

Question (4)

The square root of a number is 18. What is the number?

Explanation:

Link:

Question (5)

Which of the following cannot be a perfect square?

Explanation:

Link:

Question (6)

If 49² = 2401, then 50² is:

Explanation:

Link:

Question (7)

A square field has an area of 1024 m². Its perimeter is:

Explanation:

Link:

Question (8)

Which of the following is a perfect cube?

Explanation:

Link:

Question (9)

The cube root of 2197 is:

Explanation:

Link:

Question (10)

Which number lies exactly halfway between the perfect squares 225 and 289?

Explanation:

Link:

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