124 LearnersLast updated on May 26th, 2025
Square Root of 1445
If a number is multiplied by the same number, the result is a square. The inverse of squaring a number is finding its square root. Square roots are used in fields such as vehicle design, finance, etc. Here, we will discuss the square root of 1445.
What is the Square Root of 1445?
The square root is the inverse of the square of the number. 1445 is not a perfect square. The square root of 1445 is expressed in both radical and exponential form. In radical form, it is expressed as √1445, whereas in exponential form, it is (1445)^(1/2). √1445 ≈ 37.9987, 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 1445
The prime factorization method is used for perfect square numbers. However, for non-perfect square numbers like 1445, 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 1445 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 1445 is broken down into its prime factors.
Step 1: Finding the prime factors of 1445 Breaking it down, we get 5 x 17 x 17: 5^1 x 17^2
Step 2: Now we have found the prime factors of 1445. The second step is to make pairs of those prime factors. Since 1445 is not a perfect square, the digits of the number can’t be grouped in complete pairs.
Therefore, calculating 1445 using prime factorization alone isn't straightforward.
Square Root of 1445 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 1445, we need to group it as 45 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 less than or equal to 14. Now the quotient is 3; after subtracting 9 from 14, the remainder is 5.
Step 3: Now let us bring down 45, 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 the sum of the dividend and quotient. Now we have 6n as the new divisor, and we need to find the value of n.
Step 5: The next step is finding 6n × n ≤ 545. Let us consider n as 9, now 69 x 9 = 621.
Step 6: Subtract 545 from 621; the difference is negative, so we need to try n as 8. So, 68 x 8 = 544.
Step 7: Subtracting 544 from 545, the difference is 1, and the quotient is 38.
Step 8: Since the remainder is less than the divisor, add a decimal point. Adding the decimal point allows us to add two zeros to the dividend. Now the new dividend is 100.
Step 9: The new divisor is 760 because 760 x 1 = 760.
Step 10: Subtracting 760 from 1000, we get a result of 240.
Step 11: Continue these steps until we get two decimal places.
So the square root of √1445 ≈ 37.998
Square Root of 1445 by Approximation Method
The approximation method is another method 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 1445 using the approximation method.
Step 1: Now we have to find the closest perfect square of √1445.
The smallest perfect square less than 1445 is 1444, and the largest perfect square greater than 1445 is 1521. √1445 falls somewhere between 38 and 39.
Step 2: Now we need to apply the formula: (Given number - smallest perfect square)/(Next perfect square - smallest perfect square)
Using the formula (1445 - 1444) / (1521 - 1444) = 1/77 ≈ 0.01298 Adding this to the lower bound, we get 38 + 0.01298 = 38.01298.
So the square root of 1445 is approximately 38.01.
Common Mistakes and How to Avoid Them in the Square Root of 1445
Students make mistakes while finding the square root, such as forgetting about the negative square root or skipping steps in the long division method. Now let us look at a few of these mistakes 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 focus on the positive square root, as it is the required one in many practical applications.
For example: √50 = 7.07, 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 common mistake. To resolve this, teach students to simplify the numbers inside the square root first.
For example: √(12+24) ≠ √12 + √24. The correct way is √(12+24) = √36.
Mistake 3
Not finding the correct value of a non-perfect square
The first step to teach students is to simplify the numbers inside the square root. This is crucial to prevent mistakes in identifying approximate values.
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 root and square root regularly, as this will help them avoid confusion.
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. This may occur in subtraction or elsewhere.
Square Root of 1445 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √1445?
The area of the square is approximately 1445 square units.
Explanation
The area of a square = side^2.
The side length is given as √1445.
Area of the square = side^2 = √1445 x √1445 = 1445.
Therefore, the area of the square box is approximately 1445 square units.
Problem 2
A square-shaped building measuring 1445 square feet is built; if each of the sides is √1445, what will be the square feet of half of the building?
722.5 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 1445 by 2 = 722.5.
So half of the building measures 722.5 square feet.
Problem 3
Calculate √1445 x 5.
189.994
Explanation
The first step is to find the square root of 1445, which is approximately 37.9987.
The second step is to multiply 37.9987 by 5.
So 37.9987 x 5 = 189.994.
Problem 4
What will be the square root of (1445 + 100)?
The square root is approximately 40.25
Explanation
To find the square root, we need to find the sum of (1445 + 100). 1445 + 100 = 1545, and then √1545 ≈ 40.25.
Therefore, the square root of (1445 + 100) is approximately ±40.25.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √1445 units and the width ‘w’ is 38 units.
The perimeter of the rectangle is approximately 151.9974 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√1445 + 38) = 2 × (37.9987 + 38) = 2 × 75.9987 = 151.9974 units.
FAQ on Square Root of 1445
1.What is √1445 in its simplest form?
2.Mention the factors of 1445.
3.Calculate the square of 1445.
4.Is 1445 a prime number?
5.1445 is divisible by?
6.How does learning Algebra help students in Vietnam make better decisions in daily life?
7.How can cultural or local activities in Vietnam support learning Algebra topics such as Square Root of 1445?
8.How do technology and digital tools in Vietnam support learning Algebra and Square Root of 1445?
9.Does learning Algebra support future career opportunities for students in Vietnam?
Important Glossaries for the Square Root of 1445
- Square root: A square root is the inverse of squaring a number. For example: 4^2 = 16, and the inverse of the square is the square root, which is √16 = 4.
- Irrational number: An irrational number is one 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, but the positive square root is more prominent due to its uses in the real world. This is known as the principal square root.
- Prime factorization: Breaking down a number into its basic prime number multipliers is known as prime factorization. For example, for 1445, it is 5 × 17 × 17.
- Long division method: A step-by-step method used to find the square root of non-perfect squares by grouping numbers and determining the closest possible root.
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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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