Last updated on May 26th, 2025
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.
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.
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:
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.
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.
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.
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.
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.
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.
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
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.
Calculate √1470 × 5.
Approximately 191.605
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
What will be the square root of (1370 + 100)?
The square root is 39.
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.
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.
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√1470 + 38) ≈ 2 × (38.321 + 38) ≈ 2 × 76.321 = 152.642 units.
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.
: He loves to play the quiz with kids through algebra to make kids love it.