**Square Root and Cube Root** questions are important parts of **quantitative aptitude section** in various competitive exams. Solving these questions can be tricky if you do not possess good practice. It is essential to understand how these questions are solved to ace various competitive examinations.

*Square Root and Cube Root problems are asked in exams like:*

**UPSC CSE**- Defence Exams like (
**AFCAT**,**NDA**,**CDS**) - State PSC Exams
**GATE**- GRE
- MAT
**Bank**(PO & Clerk) Exams**SSC**(CGL, 10+2, Steno, FCI, CPO, Multitasking)- LIC (AAO & ADO)
- RRB

Start your preparation by solving these questions. In this blog, we will go over the fundamentals of Square Root and Cube Root problems, as well as the types of questions asked in previous year exams and how to approach them. This will help you clear your basics and answer these Square Root and Cube Root questions.

Table of Contents

## What is Square Root and Cube Root? What are Square Root and Cube Root Problems?

The square root and cube root are mathematical operations, that involve finding a number that, when raised to a certain power, gives a specific result. Square root and cube root problems involve finding the square root or cube root of a given number, solving equations involving these roots, or solving expressions containing these roots. Here are some questions along with the formula that you can practice on square root and cube root.

**How to Find the Square Root and Cube Root?**

To determine the square root of a number, we have to identify the number that was squared to get the original value. For instance, if we have to find the square root of 16, then it is easy to figure out that the number is obviously 4. Because when we multiply 4*4, we get the result 16. Hence, √16 = 4.

**Also Read: BODMAS Questions**

Similarly, in the case of finding the cube root, consider the example of 64, where a cube of 4 results in 64. Therefore, the cube root of 64 is 4. Now, it is easy to find square roots and cube roots of smaller numbers like this. However, in the case of larger numbers, this is not a feasible option. In the case of a large number, the prime factorization method will help to solve the question.

**Square Root and Cube Root Formulas**

**Square Root Formula** : If x^{2} = y, we say that the square root of y is x and we write y = x.

**Cube Root Formula**: The cube root of a given number x is the number whose cube is x. We, denote the cube root of x by x.

**Square Root and Cube Root Table**

Memorizing square root and cube root is a great way to solve these types of questions quickly. It is not possible to remember the square root and cube root of every number, but you can remember the roots of a few numbers from 1 to 15. The square root and cube root for the same is listed below.

Number | Square root (√) | Cube root (∛) |

1 | 1.000 | 1.000 |

2 | 1.414 | 1.260 |

3 | 1.732 | 1.442 |

4 | 2.000 | 1.587 |

5 | 2.236 | 1.710 |

6 | 2.449 | 1.817 |

7 | 2.646 | 1.913 |

8 | 2.828 | 2.000 |

9 | 3.000 | 2.080 |

10 | 3.162 | 2.154 |

11 | 3.317 | 2.224 |

12 | 3.464 | 2.289 |

13 | 3.606 | 2.351 |

14 | 3.742 | 2.410 |

15 | 3.873 | 2.466 |

## 30 + Square Root and Cube Root Questions and Answers

**Q1.** Find the Square root of √289

Ans. The Square root of √289 is 17

**Q2. **Find the Square root of √0

Ans. The Square root of √0 is 0

**Q3.** Find the Square root of √121

Ans. The Square root of √121 is 11

**Q4.** Find the Square root of √256

Ans. The Square root of √256 is 16

**Q5.** Find the Square root of √169

Ans. The Square root of √169 is 13

**Q6.** Find the Square root of √49

Ans. The Square root of √49 is 7

**Q7.** Find the Square root of √25

Ans. The Square root of √25 is 5

**Q8.** Find the Square root of √196

Ans. The Square root of √196 is 14

**Q9.** Find the Square root of √9

Ans. The Square root of √9 is 3

**Q10.** Find the Square root of √100

Ans. The Square root of √100 is 10

**Q11. **Find the Cube root of ∛64

Ans. The cube root of ∛64 is 4**Q12. **Find the Cube root of ∛343

Ans.The cube root of ∛343 is 7

**Q13. **Find the Cube root of ∛729

Ans. The cube root of ∛729 is 9**Q14. **Find the Cube root of ∛1728

Ans. The cube root of ∛729 is 12**Q15. **Find the Cube root of ∛9261

Ans. The cube root of ∛9261 is 21**Q16. **Find the Cube root of ∛4096

Ans. The cube root of ∛40961 is 16**Q17. **Find the Cube root of ∛8000

Ans. The cube root of ∛8000 is 20**Q18. **Find the Cube root of ∛3375

Ans. The cube root of ∛3375 is 15**Q19. **Find the Cube root of ∛-216

Ans. The cube root of ∛-216 is -6**Q20. **Find the Cube root of ∛-512

Ans. The cube root of ∛-512 is -8

**Q21. **What is the cube root of 2197?

**Ans. **The cube root of 2197 is 13.

**Q22. **What approximate value will come (?) in the following equation?

17.32% of 190 – 3 & redic;26.881 = ?

**Ans. **The approximate value that will come (?) in the above equation is 29.3

**Q23.** What is the cube root of 0.000216?

**Ans.** The cube root of 2197 is 0.06.

**Q24.** Find the least number by which 750 should be multiplied so that it becomes a perfect cube.

**Ans.** Using the prime factorization method the least number by which 750 should be multiplied is 36.

**Q25.** Find the value of & redic;0.64 + & redic;1.44 + & redic;0.0009.

**Ans.** The value of & redic;0.64 + & redic;1.44 + & redic;0.0009 is 2.03.

**Q26.** Which is the smallest number, with which 600 should be multiplied so that it becomes a perfect square?

**Ans.** The smallest number, with which 600 should be multiplied so that it becomes a perfect square is 6.

**Q27.** In a class each of the students contributed as many paise as there are number of students. If the total collection was Rs. 169, what was the number of students in the class?

**Ans.** The smallest number, with which 600 should be multiplied so that it becomes a perfect square is 130.

**Q28.** A person wants to arrange his colleagues in the form of a perfect square, but he finds there are 9 persons too many. What will be the total number of persons in front row, if the total number of persons with him is 2410?

**Ans.** The total number of persons in front row will be 49.

**Q29.** If &redic;15625 = 125, then the value of (&redic;156.25 + &redic;1.5625 + &redic;0.015625 + &redic;0.00015625) is

**Ans.** The value of (&redic;156.25 + &redic;1.5625 + &redic;0.015625 + &redic;0.00015625) is 13.8875

**Q30.** An army man wants to arrange his men in the form of a perfect square, but he finds there are 64 men too many. What will be the total number of men in the front row, if the total number of men with him is 15440?

**Ans.** The total number of men in the front row will be 124.

## Tips to Solve Square Root and Cube Root Questions

Following are some tips to solve Square Root and Cube Root questions-

- Memorize square roots and cube roots upto a certain range to solve the questions quickly.
- Practice multiple questions to develop a group on these types of questions.
- Make use of the prime factorization method to solve large numbers.

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## FAQs

**Is it hard to solve square root and cube root questions?**

No, with regular practice you can easily solve these types of questions. Also, you can remember the roots upto a certain range of number like 1-15.

**How to find square root?**

You can find the square root and cube root of small numbers by determining the number that is squared to get the original number. For larger numbers, you can use the prime factorization method.

**In which exams does these questions come?**

There are various competitive exams like GATE, GRE, MAT, bank exams, railway exams, etc. in which these types of questions come.

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