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Best explanation to understand and solve the square root and cube root

In this section you will learn about the topic SQUARE ROOT AND CUBE ROOT. This topic will be known by many of you since you have learned it in your higher secondary schools.

This is somewhat complicated topic. It will be easy if you know the concept clearly and also you should know some tricks and formulas to solve these problems. 

But no need to worry about this task because we have made it easy for you.

We have given you all the important formulas, explanation of important terms and also the quick method to solve these problems.

So read this article completely and know more about square root and cube root.

This will be one of the important topics in any competitive exams and bank exams. So don’t miss the opportunity to know more about this topic.

What is square root?

A square root is nothing but the value that we get when multiplying a number by itself.

For example: 42= 4 x 4  = 16

The symbol of square root is

For example: 4

What is a cube root?

A cube root is nothing but the value that we get when multiplying a number by itself twice.

For example: 43= 4 x 4 x 4 = 64

The symbol of cube root is 3

For example: 34

How to calculate square root?

To find the square root we use a simple method called factorisation method. But there is another important method called DIVISION METHOD.

This method is a little complicated so we have given you a clear explanation with step by step procedure.

How to calculate square root by factorisation method?

To find the square root of a number which is a perfect square, express the number as the product of prime factors. Now, take the product of these prime factors choosing one out of every pair of the same primes.

How to find square root by division method?

Step 1: Group the digits of the number in the pairs of two digits starting from the right-hand side. For example, if the number is 330625, there would be three pairs of digits which include 33, 06, and 25. Each pair of digits and the remaining digit if any is called a period, so there are three periods.

Step 2: Find a number whose square is either equal to or less than the first pair or period on the left of the number. For example: the square of a number ≤ 33. In this case, 5*5 = 25 ≤ 33. Use this number (5) as a divisor and also as the quotient.

Apti Square Roots and Cube Roots

Step 3: Subtract the product of the divisor and the quotient from the first pair and put the next pair to the right of the remainder. This number becomes the new dividend.

Apti Square Roots and Cube Roots

Step 4: Create new divisor by taking two times the quotient and annexing it with a suitable digit which is also taken as the next digit of the quotient. The product of this new divisor and the digit should be equal to or less than the new dividend.

Apti Square Roots and Cube Roots

Now annexing a new digit 7 with 10, because if we annexing a digit less than 7, the product of the new divisor (it can be either 101, 102, 103,… 106) and the annexing digit will not reach up to the nearby value. Therefore 107 is treated as a new divisor, and it will give a nearby value to the new dividend.

Step 5: Repeat the 2, 3 and 4th step till all the pairs or periods are taken up. The quotient so obtained is the required square root of the given number.

Apti Square Roots and Cube Roots

How to find the square root of numbers in the decimal form

Step 1: Make the number of decimal places even by placing a zero on the right of the decimal part, if required. For example, 41.2 = 41.20 (0 is added to make the decimal places even).

Step 2: In the integral part make the pairs or periods like we made in the above example.

that is 41 is a pair

Step 3: In the decimal part, mark the periods on every pair of digits starting with the first decimal place. That is 20 is a pair

Step 4: Now, find the square root by long division method.

Step 5: Place the decimal point in the square root as soon as the integral part is exhausted.

What is the determination of cube root?

Determination of Cube Root: Resolve the given number as the product of prime factors and take the product of prime factors, choosing one out of three of the same prime factors.

What are points to remember while doing the aptitude in square root and cube root?

  1. If a2 = b, we say that square root of b is “a” and we write it as √͞b=a.
  2. The symbol √ is used to denote the square root of a number.
  3. The cube root of a given number x is the number whose cube is x. We denote the cube root of a by 3√X .

These are the important terms and formulas to calculate square roots and cube roots.

If you know this concept you can easily solve these problems in your exams. We also have a set of aptitude questions on our website.

You can take up the test and practice for your exams. This will help you to score high in your exams. You can also get a clear idea about this topic.