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Test: Square Root And Cube Root- 1 - CAT MCQ


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10 Questions MCQ Test Quantitative Aptitude (Quant) - Test: Square Root And Cube Root- 1

Test: Square Root And Cube Root- 1 for CAT 2026 is part of Quantitative Aptitude (Quant) preparation. The Test: Square Root And Cube Root- 1 questions and answers have been prepared according to the CAT exam syllabus.The Test: Square Root And Cube Root- 1 MCQs are made for CAT 2026 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Square Root And Cube Root- 1 below.
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Test: Square Root And Cube Root- 1 - Question 1
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Detailed Solution for Test: Square Root And Cube Root- 1 - 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 for Test: Square Root And Cube Root- 1 - 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 for Test: Square Root And Cube Root- 1 - Question 3

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

Detailed Solution for Test: Square Root And Cube Root- 1 - 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 for Test: Square Root And Cube Root- 1 - 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 for Test: Square Root And Cube Root- 1 - 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 for Test: Square Root And Cube Root- 1 - Question 7

    Use last-digit rule

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

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

    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.

    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.

    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 for Test: Square Root And Cube Root- 1 - 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 for Test: Square Root And Cube Root- 1 - 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

Final Answer:
? = 100

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 for Test: Square Root And Cube Root- 1 - 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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