124 LearnersLast updated on May 26th, 2025
Square Root of 1420
If a number is multiplied by the same number, the result is a square. The inverse of the square is a square root. The square root is used in the fields of vehicle design, finance, etc. Here, we will discuss the square root of 1420.
What is the Square Root of 1420?
The square root is the inverse of the square of the number. 1420 is not a perfect square. The square root of 1420 is expressed in both radical and exponential form. In the radical form, it is expressed as √1420, whereas (1420)^(1/2) is in exponential form. √1420 ≈ 37.6692, which is an irrational number because it cannot be expressed as p/q, where p and q are integers and q ≠ 0.
Finding the Square Root of 1420
The prime factorization method is used for perfect square numbers. However, the prime factorization method is not used for non-perfect square numbers where the long-division method and approximation method are used. Let us now learn the following methods:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 1420 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 1420 is broken down into its prime factors.
Step 1: Finding the prime factors of 1420 Breaking it down, we get 2 x 2 x 5 x 71: 2² x 5 x 71
Step 2: Now we have found the prime factors of 1420. The second step is to make pairs of those prime factors. Since 1420 is not a perfect square, the digits of the number can’t be grouped in pairs completely.
Therefore, calculating the square root of 1420 using prime factorization does not give an exact result.
Square Root of 1420 by Long Division Method
The long division method is particularly used for non-perfect square numbers. In this method, we should check the closest perfect square number for the given number. Let us now learn how to find the square root using the long division method, step by step.
Step 1: To begin with, we need to group the numbers from right to left. In the case of 1420, we need to group it as 20 and 14.
Step 2: Now we need to find n whose square is less than or equal to 14. We can use n = 3 because 3² = 9, which is less than 14. The quotient is 3, and after subtracting 9 from 14, the remainder is 5.
Step 3: Now let us bring down 20, which is the new dividend. Add the old divisor with the same number, 3 + 3, to get 6, which will be our new divisor.
Step 4: The new divisor will be 6n. We need to find the value of n.
Step 5: Find 6n × n ≤ 520. Let us consider n as 8, now 68 x 8 = 544.
Step 6: Subtract 520 from 544, the difference is negative, so we try n as 7. 67 x 7 = 469.
Step 7: Subtracting 469 from 520 gives 51, and the quotient now is 37.
Step 8: Since the dividend is less than the divisor, we need to add a decimal point. Adding the decimal point allows us to add two zeroes to the dividend. Now the new dividend is 5100.
Step 9: Now we need to find the new divisor, which is 754, because 754 x 7 = 5278.
Step 10: Subtracting 5278 from 5100 gives a negative result, so we try n as 6.
Step 11: Continue doing these steps until we get two numbers after the decimal point. Suppose if there is no decimal value, continue until the remainder is zero.
So the square root of √1420 is approximately 37.67.
Square Root of 1420 by Approximation Method
The approximation method is another method for finding the square roots. It is an easy method to find the square root of a given number. Now let us learn how to find the square root of 1420 using the approximation method.
Step 1: Now we have to find the closest perfect square to √1420.
The smallest perfect square below 1420 is 1369, and the largest perfect square above 1420 is 1444. √1420 falls somewhere between 37 and 38.
Step 2: Now we need to apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square).
Using the formula: (1420 - 1369) / (1444 - 1369) = 51 / 75 = 0.68 Using the formula, we identified the decimal point of our square root. The next step is adding the value we got initially to the decimal number, which is 37 + 0.68 = 37.68.
So the square root of 1420 is approximately 37.68.
Common Mistakes and How to Avoid Them in the Square Root of 1420
Students make mistakes while finding the square root, such as forgetting about the negative square root or skipping long division methods, etc. Now let us look at a few of these mistakes that students tend to make in detail.
Mistake 1
Forgetting about the negative square root
It is important to make students aware that a number has both positive and negative square roots. However, we will be considering only the positive square root, as it is the required one.
For example, √50 = 7.07, but there is also -7.07, which should not be forgotten.
Mistake 2
Not adding the square root symbol in proper places
Not using the square root symbol properly is another mistake that children make. To resolve this, we need to teach children that simplifying the numbers inside the square root is important before moving on to the next step.
For example, √(12+24) ≠ √12 + √24. The right way is √(12+24) = √36.
Mistake 3
Not finding the correct value of a non-perfect square
The first step that needs to be taught to children is to simplify the numbers inside the square root. This is important so that students do not make mistakes while identifying the approximate value.
For example, √50 ≠ 7, the correct answer is √50 ≈ 7.071.
Mistake 4
Confusing the square root symbol with the cube root
Students need to be taught the difference between cube roots and square roots constantly, as this will help them avoid mistakes.
For example, √50 and ∛50 are different.
Mistake 5
Making mistakes in long division
Finding a square root using the long division method involves many steps. Due to this, many students might skip a step accidentally, which results in a wrong answer at the end of the sum. This may happen in subtraction or elsewhere.
Square root of 1420 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √420?
The area of the square is approximately 420 square units.
Explanation
The area of the square = side².
The side length is given as √420.
Area of the square = side² = √420 × √420 ≈ 20.4939 × 20.4939 = 420
Therefore, the area of the square box is approximately 420 square units.
Problem 2
A square-shaped building measuring 1420 square feet is built; if each of the sides is √1420, what will be the square feet of half of the building?
710 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 1420 by 2, we get 710.
So half of the building measures 710 square feet.
Problem 3
Calculate √1420 × 5.
Approximately 188.346
Explanation
The first step is to find the square root of 1420, which is approximately 37.6692.
The second step is to multiply 37.6692 by 5.
So 37.6692 × 5 ≈ 188.346
Problem 4
What will be the square root of (420 + 25)?
The square root is 21
Explanation
To find the square root, we need to find the sum of (420 + 25). 420 + 25 = 445, and then √445 ≈ 21.
Therefore, the square root of (420 + 25) is approximately ±21.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √420 units and the width ‘w’ is 45 units.
We find the perimeter of the rectangle as approximately 131 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√420 + 45) ≈ 2 × (20.4939 + 45) ≈ 2 × 65.4939 ≈ 131 units.
FAQ on Square Root of 1420
1.What is √1420 in its simplest form?
2.Mention the factors of 1420.
3.Calculate the square of 1420.
4.Is 1420 a prime number?
5.1420 is divisible by?
6.How does learning Algebra help students in United Arab Emirates make better decisions in daily life?
7.How can cultural or local activities in United Arab Emirates support learning Algebra topics such as Square Root of 1420?
8.How do technology and digital tools in United Arab Emirates support learning Algebra and Square Root of 1420?
9.Does learning Algebra support future career opportunities for students in United Arab Emirates?
Important Glossaries for the Square Root of 1420
- Square root: A square root is the inverse of a square. Example: 4² = 16, and the inverse of the square is the square root, that is, √16 = 4.
- Irrational number: An irrational number is a number that cannot be written in the form of p/q, where q is not equal to zero and p and q are integers.
- Principal square root: A number has both positive and negative square roots; however, it is always the positive square root that has more prominence due to its uses in the real world. That is why it is also known as the principal square root.
- Prime factorization: The process of expressing a number as a product of its prime factors. For example, the prime factorization of 1420 is 2² × 5 × 71.
- Long division method: A step-by-step process used to find the square root of a number, especially useful for numbers that are not perfect squares.
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Jaskaran Singh Saluja
About the Author
Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.
Fun Fact
: He loves to play the quiz with kids through algebra to make kids love it.
