Square Root and Cube Root: Definition, Sample Questions and Tips

In Mathematics, a Square Root is a factor root of a number, which produces the original number when multiplied by itself. For example, the Square Root of 25 is 5, because when 5 is multiplied by itself, we get 25.

Calculating Square Roots of a Number Manually

A clear understanding of square numbers is essential before we proceed with a number's square root. A number when multiplied by itself, becomes a square number. The Square Root is the number which is multiplied by itself to form a square.

Square Roots cannot be memorised always. One needs to know the method to calculate. The methods that are helpful to find out the Square Roots of a number are given below:

• Repeated Subtraction Method: In this method, equal numbers of items are subtracted from a large group. To calculate odd numbers whose total is a natural number, we have to keep subtracting 1, 3, 5, 7, 9... till we arrive at 0. Then we need to count on how many times subtraction is done to get 0. This counting is the square root of the number.
• The method of Prime Factorisation: In this method, by successive division, first, we have to derive the number and, after that, need to find out the prime factors of the number. Derived prime factors need to be paired in that way, where factors are equal in both the pairs.
• Long Division method: This method is used in such cases where square numbers are in three digits or more, and we have to divide it by two digits or more. In this method, we have to divide, then multiply, then subtract, and finally bring down the next number.

Once we learn how to find out the square roots of any given number by following these above mentioned three methods, we can easily solve any problems relating to square roots in Quantitative Aptitude. Square and square roots chapters are easily scoring chapters for your examination.

Let's illustrate the square root of numbers with the help of examples:

Example 1:

• 3 multiplied by 3 is equal to 9
• We can also write 3x3 in a shorter way, such as 33
• This method is called 3 squared or 3 to the 2nd power

Example 2:

• 4 multiplied by 4 is equal to 16
• We can also write 4x4 in a shorter way, such as 44
• This method is called as 4 squared or 4 to the 2nd power

Example 3:

• 5 multiplied by 5 is equal to 25
• We can also write 5x5 in a shorter way, such as 55
• This method is called as 5squared or 5 to the 2nd power

Also Read:

The cube of a number can be multiplied by itself three times, and the answer produced is the original value. Cube root of any number can be found by a straightforward method, known as the prime factorisation method. However, the prime factorisation method is applicable for perfect cubes. Thus, if we know the volume of the cube, we can easily find its length using the cube root formula.

What is the Symbol of Cube Root?

A cube root is denoted by symbol 3√. For example:

• Cube root of 7 can be represented as 3√7.

• Cube root of 11 can be represented as 3√11. 

Also Read: MBA Preparation: Tips to Prepare for MBA Entrance Exams

As mentioned earlier, cube root gives a value that can be cubed to get the original value. For instance, the cube of ‘a’ would give a value of ‘b’, which can be represented as 3√a = b. However, this is possible only when we find the cube roots of perfect numbers. The table below mentions the perfect cubes of some of the numbers:

Calculating or finding the cubes of imperfect numbers is easy, but the same for imperfect numbers is not that easy. The table below mentions the cube roots of different numbers, which would help students solve problems on cube roots.

How to Find the Cube Root?

Mentioned below are the two types of methods used for calculating cube root:

• Prime factorisation method –

The example to better understand the calculation of cube root by prime factorisation method is as follows:

2744 = 2x2x2x7x7x7 = (2x7)³ = ³√2744 = 2x7 = 14

• Division method –

Estimating the cube root using the division method is similar to that of a manual square method or a long division method. We will have to make a pair of similar three digits from back to front. The next step is to search for the number whose cube root is less than or equal to the stated number. Then subtract the obtained number from the given number. The next step would be to find the multiplication factor for the next long division method and continue with the above process to find the number’s cube root. Usually, this method of calculating the cube root is used for those numbers which are not a perfect cube number. For instance, find the cube root of 343 with the division method. 

Hence, 343 = 7x7x7

Read More:

• Permutation and Combination
• Probability: Definition, Rules & Example
• Interest & Simple Interest Formula
• Binomial Theorems
• Mean, Mode, Median
• Mensuration Formulas
• Quantitative Aptitude Preparation for MBA

Sample question practice crucial to preparing CAT. Get here sample questions and practice tests of how to prepare for Quantitative Aptitude for CAT pdf with solutions for practice. 

Download more Free PDFs of Quantitative Aptitude Sample Questions and Answers for Practice

Q: Can we multiply Square Roots?

Q: Can Square and Square Roots cancel each other?

Q: Does a negative number of Square Roots exist?

Q: What are Square Roots' functions?

Q: Can we say a Square Root is a one-to-one function?

Q: What does the Cubes and Cube Roots chapter include?

Q: What type of questions are asked in the examination?

Q: Are Square Roots and Cube Roots different?