Square Root 1 to 100

When you multiply two numbers by the same number, their product gives the square root. We use the symbol   also known as the radical symbol to represent the square root. If,  a = b then, a a  = b2= a. For example, the square root of 49 is 7, meaning multiplying 7 with 7 gives 49. So, 49 is a square number, and 7 is the square root of 49. Let’s learn more about square roots from 1 to 100.
 

Now that we have understood square roots, let’s explore the square roots of numbers 1 to 100. Square roots are useful in geometry, physics, and daily calculations. Given below is a chart of square roots 1 to 100, let’s take a look at this.
 

Learning the square roots of numbers from 1 to 100 can make math easier and faster. Instead of calculating them every time, having a ready list helps in quick problem-solving. Let’s take a look at the complete list of square roots from 1 to 100.

Square Roots from 1 to 10

The squares of numbers between 1 and 10 are commonly used in basic calculations and measurements. By these values, we understand simple geometry concepts like the sides of squares and right-angled triangles. Let’s explore the square roots of numbers from 1 to 10.

Square Roots from 11 to 20

The square roots of numbers between 11 and 20 are often needed when dealing with slightly larger measurements and calculations. Knowing these values helps in solving math problems related to areas and perimeters.

Square Roots from 21 to 30

When learning numbers between 21 and 30, their square roots can be useful for estimation and problem-solving in algebra and geometry. These values help in simplifying calculations involving squares and square roots. Let’s check out the square roots from 21 to 30.
 

Square Roots from 31 to 40

The square root of numbers from 31 to 40 can be helpful in physics and engineering calculations. They are useful for finding approximate values when dealing with square-shaped objects or distances. Let’s go through the square roots from 31 to 40.

Square Roots from 41 to 50

Numbers from 41 to 50 have square roots that can be useful in advanced calculations and problem-solving, especially in scientific applications. Knowing these values makes it easier to work with square-based formulas. Let’s get to know the square roots from 41 to 50.

Square Roots from 51 to 60

The square roots of numbers from 51 to 60 are important in mathematical concepts related to scaling and proportions. We can use this even in estimation and approximation. Let’s take a look at the square roots from 51 to 60.

Square Roots from 61 to 70

For numbers between 61 and 70, square roots are commonly used in measurements and calculations involving larger numbers. Let’s explore the square roots from 61 to 70.

Square Roots from 71 to 80

Square roots in the range of 71 to 80 are useful when dealing with surface area, distances, and proportions. Let’s take a look at the square roots from 71 to 80.

Square Roots from 81 to 90

The numbers from 81 to 90 include perfect squares like 81, whose square root is 9. Understanding square roots in this range of numbers helps in solving quadratic equations and optimizing calculations. Let’s explore the square roots from 81 to 90.

Square Roots from 91 to 100

Numbers from 91 to 100 include the perfect square 100, which has a square root of 10. This range of square roots is useful for calculations related to percentages, statistics, and real-world problems. Let’s explore the square roots from 91 to 100.

A number multiplied by itself gives a perfect square, which is always a whole number. For example, 4 is a perfect square because 2 × 2 =4, and 9 is a perfect square because 3 × 3 = 9. Knowing the square roots of perfect squares helps kids quickly solve math problems without doing long calculations. Let’s take a look at the square roots of perfect squares.
 

The numbers that do not have whole numbers as their square roots are Non-perfect squares. For example, the square root of 2 is approximately 1.41, and the square root of 10 is about 3.16. These numbers are tricky to remember, but knowing their approximate values can help in everyday math problems. Let’s explore the square roots of non-perfect squares from 1 to 100.
 

Calculating square roots can seem tricky, but with the right methods, it gets easier. To check whether the number is a perfect square or not, we use different methods to find the square root. Let’s look at the two commonly used methods to find square roots : 

• By the Prime Factorization Method
   
• By the Division Method
   

In this method, we break down a number into its prime factors and pair them to find the square root. We use this method to find the square root of perfect square numbers. 

Steps to calculate square roots using prime factorization:

• Write the number as a product of its prime factors. For example, for 36 = 2 × 2 × 3 × 3.
   
• Pair the prime factors in groups of two. For example, (2 × 2), (3 × 3)
   
• Take one factor from each pair and multiply them together to get the square root. Example, 2 × 3 =6.
   

In this method, we find the square root of any number by a step-by-step process. This method can be used for both perfect and non-perfect squares.  

Steps to calculate square root using the division method:

• Pair the digits starting from right to left. For example, 50 is written as 50.00 (pairing 50 and 00)
   
• Find the closest square which neither less nor equal to the first number. For example, 7 × 7 =49 is less than 50. 
   
• Subtract and bring down the next pair of digits. For example, 50–49 =1, bring down 00 to make it 100.
   
• Double the quotient and use it to form a new divisor. For example, double 7 (quotient), which gives 14. Find a digit to make 14 x __ close to 100.
   
• The digit is 7, and multiplying 147 by 7 gives 1029 close to 1000. 
   
• Repeat the process if needed.
   

To master square roots, it is always better to understand the basic rules. Let’s dive into the rules for calculating square roots from 1 to 100.

Rule 1: Simplify square roots for perfect squares.

When simplifying square roots using prime factorization, we break the number into its prime factors and then pair the factors to find the square root. You can find the square root easily, as these are numbers that result from multiplying a number by itself. For example, The square root of 36 is ±6 because 6 × 6 =36.

Rule 2: Approximation for non-perfect squares.

For non-perfect squares, such as 50 or 98, finding the square root will give you an approximate value. While you can’t get an exact whole number, you can find an approximate value. You can use the division method or a calculator for precision, but here is how to approximate: 
For example, for 50, the square root is approximately 7.07. 

Rule 3: Use of fractions for roots of decimals.

When you have a decimal number, you can turn it into a fraction to make finding the square root easier. For example, the square root of 0.25 can be written as 2510 , Which simplifies to 510 or 0.5.

Rule 4: Avoid rounding errors in calculations.

While calculating square roots, especially for non-perfect squares, avoid rounding the numbers too early. For example, the square root of 50, if rounded early, can lead to incorrect answers.
 

Mastering square roots helps in improving problem-solving skills. Understanding square roots can be tricky. Here are some useful tips and tricks to help children learn square roots from 1 to 100 effectively.

• Identifying the unit digits of perfect squares

Few numbers always have the same unit digit in their squares. This trick can help in recognizing if a number is a perfect square or not. For example, numbers ending in 2, 3, 7, or 8 are not perfect squares. While numbers ending in 0, 1, 4, 5, 6, or 9 can be perfect squares.

• Divide and average method

To estimate square roots, take a guess and improve it by averaging it. For example, to approximate 40 , Start with a guess, say 6. Divide 40 ÷ 6 = 6.67. The average of  6 + 6.672 = 6.33.

• Skip large numbers by breaking them down

When calculating larger numbers, break them into smaller numbers. For example, 900 = 9 ÷ 100 = 3 × 10 =30.

Approximation: Estimating the square root value when it is not a perfect square. For example, 50 = 7.07.

Whole number: Any positive integer which does not include fractions and decimals. For example, numbers starting from 0, 1, 2, 3, and so on.

Decimal numbers: Numbers in which the whole number and fractional part are separated by a point (dot). For example, 3.5 here 3 and 5 are separated by a dot.