129 LearnersLast updated on May 26th, 2025
Square Root of 1470
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 field of vehicle design, finance, etc. Here, we will discuss the square root of 1470.
What is the Square Root of 1470?
The square root is the inverse of the square of the number. 1470 is not a perfect square. The square root of 1470 is expressed in both radical and exponential form. In the radical form, it is expressed as √1470, whereas (1470)^(1/2) in exponential form. √1470 ≈ 38.321, which is an irrational number because it cannot be expressed in the form of p/q, where p and q are integers and q ≠ 0.
Finding the Square Root of 1470
The prime factorization method is used for perfect square numbers. However, the prime factorization method is not used for non-perfect square numbers where long-division and approximation methods are used. Let us now learn the following methods:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 1470 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 1470 is broken down into its prime factors.
Step 1: Finding the prime factors of 1470 Breaking it down, we get 2 x 3 x 5 x 7 x 7: 2^1 x 3^1 x 5^1 x 7^2
Step 2: Now we found out the prime factors of 1470. The second step is to make pairs of those prime factors. Since 1470 is not a perfect square, the digits of the number can’t be grouped into pairs that yield a square.
Therefore, calculating 1470 using prime factorization alone doesn't give an exact square root.
Square Root of 1470 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 1470, we need to group it as 70 and 14.
Step 2: Now we need to find n whose square is less than or equal to 14. We can say n is '3' because 3 x 3 = 9 is lesser than 14. Now the quotient is 3, and after subtracting 9 from 14, the remainder is 5.
Step 3: Now let us bring down 70, which is the new dividend. Add the old divisor (3) with the same number to get 6, which will be part of our new divisor.
Step 4: We now have 6n as the new divisor and need to find the value of n.
Step 5: The next step is finding 6n + n ≤ 570. If n is 8, we have 68 × 8 = 544.
Step 6: Subtract 544 from 570, and the difference is 26.
Step 7: Since the dividend is less than the divisor, we need to add a decimal point. Adding the decimal point allows us to add two zeros to the dividend. The new dividend is 2600.
Step 8: Now we need to find the new divisor. If we try 65, 765 × 5 = 3825, which is too large. We try smaller numbers until it fits the requirement.
Step 9: Continuing this method will reveal the decimal places of the square root.
So the square root of √1470 ≈ 38.321.
Square Root of 1470 by Approximation Method
The approximation method is another way for finding 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 1470 using the approximation method.
Step 1: Now we have to find the closest perfect square of √1470.
The smallest perfect square less than 1470 is 1444 (38^2), and the largest perfect square more than 1470 is 1521 (39^2). √1470 falls somewhere between 38 and 39.
Step 2: Now we need to apply the formula that is (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square).
Using the formula, (1470 - 1444) ÷ (1521 - 1444) ≈ 0.321 Using the formula, we identified the decimal point of our square root. Adding the value we got initially to the decimal number, we get 38 + 0.321 = 38.321, so the square root of 1470 is approximately 38.321.
Common Mistakes and How to Avoid Them in the Square Root of 1470
Students make mistakes while finding the square root, such as forgetting about the negative square root or skipping long division methods. Now let us look at a few of those 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 taking only the positive square root, as it is the required one in most real-world applications.
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 properly is another mistake. To resolve this, we need to teach students that simplifying the numbers inside the square root is important before proceeding to the next step.
For Example: √(12 + 24) ≠ √12 + √24; the correct method 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 students is to simplify the numbers inside the square root. This ensures students do not make mistakes while identifying the approximate value.
For Example: √50 ≠ 7; the correct answer is √50 ≈ 7.071067.
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, resulting in a wrong answer at the end. This may either happen in subtracting or elsewhere in the process.
Square Root of 1470 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √1470?
The area of the square is approximately 2164.961 square units.
Explanation
The area of the square = side^2.
The side length is given as √1470.
Area of the square = side^2 = √1470 × √1470 ≈ 38.321 × 38.321 = 1468.961
Therefore, the area of the square box is approximately 1468.961 square units.
Problem 2
A square-shaped building measuring 1470 square feet is built; if each of the sides is √1470, what will be the square feet of half of the building?
735 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 1470 by 2 = 735
So half of the building measures 735 square feet.
Problem 3
Calculate √1470 × 5.
Approximately 191.605
Explanation
The first step is to find the square root of 1470, which is approximately 38.321.
The second step is to multiply 38.321 by 5.
So 38.321 × 5 ≈ 191.605
Problem 4
What will be the square root of (1370 + 100)?
The square root is 39.
Explanation
To find the square root, we need to find the sum of (1370 + 100). 1370 + 100 = 1470, and then √1470 ≈ 38.321.
Therefore, the square root of (1370 + 100) is approximately ±38.321.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √1470 units and the width ‘w’ is 38 units.
We find the perimeter of the rectangle as approximately 152.642 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√1470 + 38) ≈ 2 × (38.321 + 38) ≈ 2 × 76.321 = 152.642 units.
FAQ on Square Root of 1470
1.What is √1470 in its simplest form?
2.Mention the factors of 1470.
3.Calculate the square of 1470.
4.Is 1470 a prime number?
5.1470 is divisible by?
6.How does learning Algebra help students in Bahrain make better decisions in daily life?
7.How can cultural or local activities in Bahrain support learning Algebra topics such as Square Root of 1470?
8.How do technology and digital tools in Bahrain support learning Algebra and Square Root of 1470?
9.Does learning Algebra support future career opportunities for students in Bahrain?
Important Glossaries for the Square Root of 1470
- Square root: A square root is the inverse of a square. Example: 4^2 = 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, the positive square root is often used in real-world applications. This is known as the principal square root.
- Prime factorization: Expressing a number as the product of its prime factors is called prime factorization.
- Perimeter: The total length of the boundary of a geometric figure. In the case of a rectangle, it is calculated as 2 × (length + width).
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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
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