## Trick to find the square roots of perfect square in 3 Seconds

In most school and college exams, questions about square and cube roots are asked. Solving linear equations, quadratic equations, and factorizing equations all call for the discovery of perfect square roots and cube roots. When calculating the area, perimeter, and other properties of geometric figures, solving square roots is also helpful. This will be helpful when dealing with Pythagoras’ Theorem applications. Here we will learn trick to find the square roots of perfect square in 3 seconds.

**What benefits might students gain from locating the square roots of perfect squares?**

Finding a perfect square integer’s square root can help students better understand the idea of square roots, which is the value that, when multiplied by itself, yields the original number.

**Building mental math skills:** Students may estimate and compute square roots rapidly without the need of a calculator by learning square root methods and patterns. Their ability to calculate mentally is enhanced, which increases their problem-solving effectiveness.

**Real-world applications:** Square roots are utilized in many real-world calculations, including those for volumes, areas, and distances. Students can use their understanding of the square root of perfect squares to tackle real-world issues in disciplines like engineering, physics, and finance.

**Getting ready for higher-level mathematics:** Algebra, trigonometry, and calculus all require an understanding of square roots and their properties. Students lay a strong basis for their future math studies by understanding the square roots of perfect squares.

Easy and quick way to find the square root…

### **WHAT IS SQUARE**** & SQUARE ROOT**

#### Squaring of a number can be defined as multiplying a number by itself.

Thus, when we multiply 4 by 4 we are said to have ‘squared’ the number four. The symbol of square is represented by putting a small 2 above the number.

For example,

4^{2} = 4 x 4 = 16

From the above example we can say that 16 is the square of 4, and 4 is the **‘square root’ **of 16.

The square root of a number is the value which when multiplied to itself gives the original number.

**Trick to find square root with example**

The squares are given below. Memorize them before proceeding ahead.

The squares – numbers table:

Number | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |

Square | 1 | 4 | 9 | 16 | 25 | 36 | 49 | 64 | 81 | 100 |

** ****Suppose we need to find the square root of large numbers such as 4489.**

**Step 1:** The unit digit in this number is 9, which can be a unit digit of its square root number such as 3 or 7. see the squares – numbers table above. In that table we can see the numbers, whose square having 9 at the end are 3 or 7.

**Because, 3 ^{2} is 9 and 7^{2} is 49.**

The answer at this stage is __3 or__7.

**Step 2:** Now let’s consider the first two digits that is 44 which comes between the squares of 6 and 7, because

6^{2} < 44< 7^{2}

We can assume that **the ten’s digit** of the square root of 4489 is **the lowest among the two numbers i.e. 6****.**

Now, we need to find the unit digit between 63 or 67 which is the square root of 4489.

**Step ****3****:** Since the ten’s digit is 6 and the next number is 7, we need to multiply both the numbers like 6 x 7 = 42 and **since 42 is less than 44**** (given first 2 digits), square root of 4489 will be the bigger number between 63 and 67 i.e. 67.**

**Thus, √4489 = 67**

**Let****’****s have a look at another example, the square root of 7056.**

Now, consider the unit digit that is 6. Which all numbers have the unit digit 6 on their square roots. That are 4 and 6 because 4^{2} is 16 and 6^{2} is 36.

Now let’s consider the first two digits that is 70 which comes between the squares of 8 and 9 because of 8^{2} < 70 <9^{2}.

**We can assume that the ten’s digit of the square root of the 7056 is the lowest among the two numbers that is 8****.**

So, we need to find the unit digit of the square root of the number 7056. For that, we need between 84 and 86 which is the square root of 7056.

Since the ten’s digit is 8 and the next number is 9, we need to multiply both the numbers like 8 x 9 = 72 and **since 72 is bigger than 70,**** ****square root of 7056 will be the lesser number between 84 and 86 that is 84.**

**Thus, √7056 = 84****.**