CAT Quantitative Aptitude 2021 consists of a range of terminologies in which square root and cube root are some of the most common factors used to solve numerical problems. 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. The difficulty level of CAT 2021 Quantitative Section ranges from moderate to difficult, thus the questions framed on square and cube root sections will vary similarly in difficulty. The questions asked from Cubes and Square Root could be MCQ or TITA type.With CAT 2021 exam just around the corner, Candidates should devote at least half an hour practising cubes and square roots per day to ace the exam. Also Check CAT Syllabus

CAT Admit Card 2021 was released on Oct 27, 2021. CAT 2021 exam would be conducted on November 28, 2021. In this article, concepts, formulas along with some solved questions from the previous year for CAT QA Cube Roots and Square Roots are defined. Read the article to know more about the basics of the concept to prepare for CAT. 

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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.

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Cube Root and Square Roots of First 100 Numbers