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CAT Exam  >  CAT Test  >  Quantitative Aptitude (Quant)  >  Test: Square Root And Cube Root- 1 - CAT MCQ

Square Root And Cube Root- 1 - CAT Quant Aptitude Free MCQ Test with solutions


MCQ Practice Test & Solutions: Test: Square Root And Cube Root- 1 (10 Questions)

You can prepare effectively for CAT Quantitative Aptitude (Quant) with this dedicated MCQ Practice Test (available with solutions) on the important topic of "Test: Square Root And Cube Root- 1". These 10 questions have been designed by the experts with the latest curriculum of CAT 2026, to help you master the concept.

Test Highlights:

  • - Format: Multiple Choice Questions (MCQ)
  • - Duration: 10 minutes
  • - Number of Questions: 10

Sign up on EduRev for free to attempt this test and track your preparation progress.

Test: Square Root And Cube Root- 1 - Question 1
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Detailed Solution: Question 1

Given:
x / √512 = √648 / x

Cross-multiply:
x2 = √512 · √648 = √(512 · 648)

Compute inside the radical:
512 = 29, 648 = 23 · 34
512 · 648 = 212 · 34

So:
x2 = √(212 · 34)
= 26 · 32
= 64 · 9
= 576

Hence:
x = ±√576 = ±24

Test: Square Root And Cube Root- 1 - Question 2
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Detailed Solution: Question 2

Step 1:
We know,
22 = 4 and 2.52 = 6.25
So, 5.4756 lies between 4 and 6.25.
Hence, √5.4756 lies between 2 and 2.5.

Step 2:
Try 2.34:
(2.34)2 = (2.3 + 0.04)2
= (2.3)2 + 2 × 2.3 × 0.04 + (0.04)2
= 5.29 + 0.184 + 0.0016
= 5.4756

Step 3:
Since (2.34)2 = 5.4756,
therefore √5.4756 = 2.34


Option (d) is correct.

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Test: Square Root And Cube Root- 1 - Question 3
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If 3√5 + √125 = 17.88, then what will be the value of √80 + 6√5?

Detailed Solution: Question 3

Test: Square Root And Cube Root- 1 - Question 4
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The cube root of 0.000729 is

Detailed Solution: Question 4

To find the cube root of 0.000729, we recognize that 0.000729 can be expressed as (0.09)3.
Therefore, the cube root of 0.000729 is 0.09, which confirms that option 1 (0.09), is the correct answer.

Test: Square Root And Cube Root- 1 - Question 5
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Detailed Solution: Question 5

= (12/11) x (11/15) x (15/14)

= 12/14

= 0.85

Test: Square Root And Cube Root- 1 - Question 6
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Detailed Solution: Question 6

► Using identity, (a-b)2 = a2 + b2 - 2ab

► Here a = √7 and b = 1/√7

 
= (√7)2 + (1/√7)2 - 2. √7.1/√7

= 7 + 1/7 - 2

= 5 + 1/7

= 36/7

Test: Square Root And Cube Root- 1 - Question 7
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The square root of 16641 is:

Detailed Solution: Question 7

  1. Use last-digit rule

  • Perfect squares end with: 0,1,4,5,6,9.

  • 16641 ends with 1 → root ends with 1 or 9.

  1. Use digit-sum (9’s test) for a quick filter

  • Sum of digits = 1+6+6+4+1 = 18 → 18 ≡ 0 (mod 9) → number is a multiple of 9.

  • A perfect square that’s a multiple of 9 must have a root that’s a multiple of 3.

  • Among endings {1,9}, only 9 is a multiple of 3 → root ends with 9.

  1. Find the two bounding tens

  • 1202 = 14400, 1302 = 16900
    → √16641 is between 120 and 130.

  • With last digit 9 and within 120–130, the only candidate is 129.

  1. Quick confirm using (a−b)2 trick

  • 1292 = (130−1)2 = 1302 − 2·130 + 1 = 16900 − 260 + 1 = 16641.

Test: Square Root And Cube Root- 1 - Question 8
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Detailed Solution: Question 8


Squaring both side,
⇒ 0.0576 x a = 0.0576
⇒ a = 1

Test: Square Root And Cube Root- 1 - Question 9
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Detailed Solution: Question 9

Given Equation:
√0.000256 × ? = 1.6

Step 1: Find the square root of 0.000256
Write the number in scientific notation:
0.000256 = 256 × 10-6

Take the square root:
√(256 × 10-6) = √256 × √10-6
= 16 × 10-3
= 0.016

Step 2: Substitute into the given equation
0.016 × √? = 1.6

Step 3: Solve for ?
√? = 1.6 ÷ 0.016 = 100

Step 4: Square on both side
? = 10000
Hence, option(D) is correct

Test: Square Root And Cube Root- 1 - Question 10
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If the product of three consecutive positive integers is 15600 then the sum of the squares of these integers is 

Detailed Solution: Question 10

Let the integers be n, n+1, n+2.
n(n+1)(n+2) = 15600 → try n = 24 since 24·25·26 = 15600. So the integers are 24, 25, 26.

Sum of squares = 242 + 252 + 262
= 576 + 625 + 676
= 1877.

Answer: 1877.

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About this CAT Practice Test

This test contains 10 MCQs on Square Root And Cube Root- 1 with detailed solutions for each question. It is part of the Quantitative Aptitude (Quant) course on EduRev, designed to align with the current CAT syllabus. Each solution explains not just the correct answer but also gives you an understanding of the topic — not just to attempt the question but also help you prepare for the exam with practice.

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