CAT 2025 Preparation of Cube Roots and Square Roots: Check Important Formulas, Previous Year Solved Sample Questions, and Definitions

CAT Quantitative Aptitude 2025 consists of multiple problems in which square root and cube root are some of the most common factors. Usually, we reach out to our calculators or smartphones to compute square roots and cube roots. But what if there is no calculator or smartphone? Remembering all the Square Roots and understanding the method to calculate is very beneficial for solving CAT 2025 Quantitative Aptitude questions. 

By analyzing CAT Previous Year Question Paper, it can be said that around 2 to 3 questions could be based on the basic concepts of square and cube root.

• Square Roots cannot be memorized always, you need to know the method to calculate.
• The difficulty level of CAT 2025 Quantitative Section ranges from moderate to difficult.
• The questions asked from Cubes and Square Root could be MCQ or TITA type.

Also Read

• How to Prepare for Quantitative Aptitude
• CAT Quantitative Aptitude Syllabus
• CAT QA Mock Test

Cube Root and Square Roots of First 100 Numbers

We have provided the cube roots and square roots of first 100 numbers. This will help you know the roots of all numbers till 100. 

Also Read

• CAT Quantitative Aptitude Exam Analysis
• CAT Topic Wise Weightage for QA
• CAT Previous Year Question Paper

Want to know Tips and Tricks to Find Square Root and Cube Root?

A video by S Chand Academy explains details and helps you to solve square root and cube root questions. The video can be checked by students applying for CAT or any other exam with similar syllabus. 

What is Square Root?

A square root can be defined as a factor root of a number that is responsible to generate the primary number by multiplying it. As an example, the square root of 25 is 5, as a result when 5 is multiplied by itself, the outcome is 25. 

How to Calculate Square Roots of a Number Manually? 

It is necessary for each candidate to have a fair idea of that before proceeding with the square root. Any number becomes a square number when it is multiplied by itself to structure a square. 

What Methods Must Follow to Get the Square Root?

Below are the methods that must be followed to get the square root. 

• Repeated Subtraction Method: The same number of units are taken away from a wide range of groups. 
• Prime Factorisation Method: The prime factors can be found out after extracting the number. 
• Long Division Method: In a position where the square numbers are found in more than three digits this method is used. All I need to do is to set this in the two numbers. After that subtract the number after multiplying this. 

After finding out the value of the square root of a specific number with the above method, everyone can easily solve the problem.

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CAT QA Solved Question on Square Root 

Ques.1. What will the exact value come (?) in the following equation?

If 35–√+125−−−√=17.88, then 80−−√+65–√ =?

13. 13.41
14. 20.46
15. 21.66
16. 22.35

Answer: Option D

Solution: 35–√+125−−−√=17.88 ⇒35–√+55–√=17.88 

⇒5–√=2.235

 ∴80−−√+65–√=45–√+65–√=105–√=10×2.235=22.35

Ques.2. What is the exact value (?) for the following equation?

84.95% of 280 + √? = 253.001

1. 256
2. 324
3. 18
4. 225

Answer : Option D

Solution: 253.001=253, 84.95% of 280 + √? =253. Hence, answer is 225

Ques.3. What will be the square root of √45796 = ?

1. 196
2. 216
3. 186
4. 214

Answer : Option D

Ques.4. Find the square roots of the equation √484 + √529?

1. 43
2. 47
3. 45
4. 23

Answer : Option C

Solution: Square root of 484 is 22 and the square root of 529 is 23. By adding both, the answer will be 45.

Ques.5. Every single candidate from a class has given as much money as the number of them. How many candidates are there in the class when the overall collection is INR 64?

1. 90
2. 82
3. 80
4. None of these

Answer : Option C

Solution: The number of candidates in class is x. Every candidate gives ‘x’ paise in each. The collection will be x2 paise in total. After that the total collection that is given is INR. 64, which is 6400 paise. As per the statement of the question x2 = 6400 ⇒ x = 80. Hence, total 80 students.

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What is Cube Root?

A number’s cube root is multiplied by three times. The outcome is the main value. The prime factorisation method can be used to form perfect cubes. 

Formula of Cube Root

Prime factorisation method 

• To understand this formula check out the below calculation. 
• 2744 = 2x2x2x7x7x7 = (2x7)3 = 3√2744 = 2x7 = 14

CAT QA Solved Question on Cube Root 

Ques.1. What exact value comes (?) in the following equation?

17.32% of 190 - 3&redic;26.881 = ?

1. 12
2. 50
3. 29
4. 80

Ans : Option C

Solution: We have 17.32% of 190 - 3&redic;26.881 = ?

⇒ 17% of 190 - 3&redic;

⇒ ? = (20% - 3%) of 190 – 3= 38 – 5.7 – 3 = 29.3. So, Option C is correct. 

Ques. 2. What is the least number by which 750 is multiplied to form an exact cube?

1. 12
2. 24
3. 36
4. 48

Ans : Option C

Solution: Prime factorization of 750= (2 * 3 * 5 * 5 * 5)

It must multiply with (2 * 2) * (3 * 3) = 36.

Ques. 3. What is the value of &redic;0.64 + &redic;1.44 + &redic;0.0009? 

2. 2.03
3. 2.1
4. 2.11
5. 2.13

Ans : Option A

Solution: Given exp. = &redic;64/100 + &redic;144/100 + &redic;9/10000 = 8/10 + 12/10 + 3/100

= 0.8 + 1.2 + 0.03 = 2.03

Ques. 4. What is the smallest number, with that 600 need to be multiplied to get a perfect square?

1. 2
2. 3
3. 3.5
4. 6

Ans : Option D

Solution: 600= 5 * 5 * 3 * 2 * 2 * 2, It need to be multiplied by 3 * 2 = 6.

Ques. 5. In the class, every candidate contributed as much money as the total number of students. How many candidates will be there in the class If there is the total collection is INR 169?

1. 113
2. 112
3. 130
4. 120

Ans : Option C

Solution: Let a number of students be y. They all contributed y paisa each.

So, y * y = 16900 paisa. Hence y = 130.