**Square Roots Definition, Methods and Cube Roots List**

Read the article to get detailed information about square roots, methods to find the square roots of a number, square roots and cube roots, and a list of square roots.

Square Roots: The square root of a number is multiplying factor of a number which when multiplied by itself hives the actual number. The square root is just the opposite method of squaring a number. In squaring of a number same number is multiplied by itself giving the square of a number while in square root the original number is obtained on squaring the number. The square of any number is always a positive number while the square root of a number has both positive and negative values. We can understand the square and square root easily by taking a simple example. Suppose if ‘x’ is a square of the number ‘y’ means x × x = y but if ‘x’ is a square root of ‘y’ means x2= y.

**Square Roots**

A Square root is a number that when multiplying gives the original number. It is like a factor, both square and square roots are a type of exponent. In other square roots can be defined as the number whose value has the power of 1/2 of a number. The symbol to represent the square root is √ which is called radical in mathematics and the number inside or called the radicand. For example, suppose a number 16 which can be obtained by multiplying 4 by 4 i.e. 4 × 4 = 16 me, and 16 is a square of 4. And suppose a number √9 on squaring the number √32 = 3 so the square root of √9 is 3. Here we will discuss the square root in detail. So refer to the below content to understand the square root in a good manner.

**How to find Square Root?**

The square root of a number is the square of a number that gives the original number. When finding a square root of a number firstly we need to find whether the number is a perfect square or imperfect. A perfect square is a number that can be expressed in the form of power 2. The square root of the perfect square can be found easily by factoring it into the prime factors. If a number is an imperfect square then the long division method needs to be performed on it which is discussed below in the article.

To find the square root of a number following four methods are used:

- Square Root by Prime Factorization
- Square Root by Repeated Subtraction Method
- Square Root by Long Division Method
- Square Root by Estimation Method

We will discuss all the above four methods in detail with a suitable example.

**1. Square Root by Prime Factorisation Method**

The square root of a perfect square number can be found easily by Prime Factorisation Method. In this method, some steps need to be followed to find the square root of a number listed below:

- Divide the given number into its prime factors.
- Form pairs of similar factors such that both factors in each pair are equal.
- Take one factor from the pair.
- Find the product of the factors obtained by taking one factor from each pair.
- The product gives the square root of the given number.

64 = 2×2×2×2×2×2×2

On pairing, we get 2×2×2 = 8

So the square root of 64 is 8.

**2. Square Root by Repeated Subtraction Method**

In the Repeated Subtraction Method, the square root of a number can be found by following the below steps if a given number is a perfect square.

- Repeatedly subtract the consecutive odd numbers from the given number
- Subtract till the difference remains zero
- The number of times we subtract will be the required square root

For example, let us find the square root of the number 36

- 36 – 1 = 35
- 35 – 3 = 32
- 32 – 5 = 27
- 27 – 7 = 20
- 20 – 9 = 11
- 11 – 11 = 0

Since, the subtraction is done 6 times, hence the square root of 36 is 6

**3. Square Root by Long Division Method**

Using the long division method the square roots of imperfect squares can be found easily. The method can be understood by the below steps.

- Place a bar over every pair of digits of the number starting from the units’ place (right-side).
- Then we divide the left-most number by the largest number whose square is less than or equal to the number in the left-most pair.

Calculate the square root of 17.64

The square root of 17.64 by the long division method is found to be 4.2

**4. Square Root by Estimation Method**

This method used approximation to find the square root of a number. The square root can be found by guessing the approximate value.

For example, we know that the square root of 4 is 2 and the square root of 9 is 3, thus we can guess, that the square root of 5 will lie between 2 and 3.

But, we need to check the value of √5 is nearer to 2 or 3. Let us find the squares 2.2 and 2.8.

2.22 = 4.84

2.82 = 7.84

Since the square of 2.2 gives 5 approximately, thus we can estimate the square root of 5 is equal to 2.2 approximately.

**Square Root 4**

The square root of 4 is denoted by √4. We know that 4 is a perfect square whose square root can be found easily by the prime factorization method or repeated subtraction method. The square root of 4 is 2. But the square roots have two values always positive and negative as we already discussed. So √4 has two values +2 and -2.

**Square roots 1 to 30**

As we discussed the square riots can be found easily using the four methods mentioned above. The list of square roots from 1 to 30 is mentioned here.

Square Roots 1 to 30 |
||

√1 | = | 1 |

√2 | = | 1.4142 |

√3 | = | 1.732 |

√4 | = | 2 |

√5 | = | 2.236 |

√6 | = | 2.4494 |

√7 | = | 2.6457 |

√8 | = | 2.8284 |

√9 | = | 3 |

√10 | = | 3.1622 |

√11 | = | 3.3166 |

√12 | = | 3.4641 |

√13 | = | 3.6055 |

√14 | = | 3.7416 |

√15 | = | 3.8729 |

√16 | = | 4 |

√17 | = | 4.1231 |

√18 | = | 4.2426 |

√19 | = | 4.3588 |

√20 | = | 4.4721 |

√21 | = | 4.5825 |

√22 | = | 4.6904 |

√23 | = | 4.7958 |

√24 | = | 4.8989 |

√25 | = | 5 |

√26 | = | 5.099 |

√27 | = | 5.1961 |

√28 | = | 5.2915 |

√29 | = | 5.3851 |

√30 | = | 5.4772 |

**Square Roots and Squares**

**Square Roots and Cube Roots**

**Examples:**

**Square Roots: FAQs**

**Que.1 What are squares?**

**Ans**– The squares are a twice multiplication of the number itself. For example, 25 is a square of 5 i.e. 5×5 = 25

**Que.2 What are square roots?**

**Ans**– Square root is just opposite to square. Is the 1/2 power of a number. For example, the square root of 9 is 3 i.e. √9 = 3