107 LearnersLast updated on May 26th, 2025
Square Root of 1.2
If a number is multiplied by itself, the result is a square. The inverse of squaring a number is finding its square root. The square root is used in fields such as engineering, finance, and physics. Here, we will discuss the square root of 1.2.
What is the Square Root of 1.2?
The square root is the inverse of squaring a number. 1.2 is not a perfect square. The square root of 1.2 is expressed in both radical and exponential form. In the radical form, it is expressed as √1.2, whereas 1.2^(1/2) in the exponential form. √1.2 ≈ 1.095445, 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 1.2
The prime factorization method is used for perfect square numbers. However, for non-perfect square numbers, we use methods like the long division method and approximation method. Let us now learn the following methods:
- Long division method
- Approximation method
Square Root of 1.2 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: Group the numbers from right to left. In the case of 1.2, consider it as 1.20.
Step 2: Find a number n whose square is less than or equal to 1. Here, n = 1 because 1 × 1 = 1. Subtracting, we get a remainder of 0.
Step 3: Bring down 20, making it the new dividend. Double the previous quotient (1) to get the new divisor, which is 2.
Step 4: Find n such that 2n × n ≤ 20. Here, n = 4, because 24 × 4 = 96.
Step 5: Subtract 96 from 120 to get 24. Bring down two zeros to make it 2400.
Step 6: Double the entire quotient (10.4) to get 208. Find the new n such that 208n × n ≤ 2400.
Step 7: Continue the steps until you achieve the desired precision. So, √1.2 ≈ 1.095445.
Square Root of 1.2 by Approximation Method
The approximation method is another method for finding square roots, and it is an easy method to find the square root of a given number. Let's learn how to find the square root of 1.2 using the approximation method.
Step 1: Identify the closest perfect squares around 1.2. These are 1 (1^2) and 1.44 (1.2^2). Thus, √1.2 is between 1 and 1.2.
Step 2: Apply the approximation formula: (Given number - smaller perfect square) / (larger perfect square - smaller perfect square). For 1.2, (1.2 - 1) / (1.44 - 1) = 0.2 / 0.44 ≈ 0.454545.
Step 3: Add this to the smaller perfect square's root: 1 + 0.454545 = 1.454545. Thus, √1.2 ≈ 1.095445, which is more accurate than the approximation.
Common Mistakes and How to Avoid Them in the Square Root of 1.2
Students often make mistakes when finding square roots, such as forgetting about the negative square root or misapplying methods. Let's look at a few of these mistakes in detail.
Mistake 1
Forgetting about the negative square root
Students should remember that a number has both positive and negative square roots. However, we often use only the positive square root in practical applications.
For example, √1.2 ≈ ±1.095445, but we typically use the positive root.
Square root of 1.2 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √1.2?
The area of the square is approximately 1.2 square units.
Explanation
The area of the square = side^2.
The side length is given as √1.2.
Area of the square = (√1.2)^2 = 1.2.
Therefore, the area of the square box is approximately 1.2 square units.
Problem 2
A square-shaped building measuring 1.2 square feet is built; if each of the sides is √1.2, what will be the square feet of half of the building?
0.6 square feet
Explanation
We can divide the given area by 2 since the building is square-shaped.
Dividing 1.2 by 2 = 0.6.
So, half of the building measures 0.6 square feet.
Problem 3
Calculate √1.2 × 5.
Approximately 5.477225.
Explanation
First, find the square root of 1.2, which is approximately 1.095445.
Then multiply by 5. So, 1.095445 × 5 ≈ 5.477225.
Problem 4
What will be the square root of (0.8 + 0.4)?
The square root is approximately 1.095445.
Explanation
To find the square root, sum (0.8 + 0.4) = 1.2, and then find √1.2, which is approximately 1.095445.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √1.2 units and the width ‘w’ is 1 unit.
The perimeter of the rectangle is approximately 4.19089 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√1.2 + 1) = 2 × (1.095445 + 1) = 2 × 2.095445 ≈ 4.19089 units.
FAQ on Square Root of 1.2
1.What is √1.2 in its simplest form?
2.Mention the factors of 1.2.
3.Calculate the square of 1.2.
4.Is 1.2 a prime number?
5.1.2 is divisible by?
6.How does learning Algebra help students in India make better decisions in daily life?
7.How can cultural or local activities in India support learning Algebra topics such as Square Root of 1.2?
8.How do technology and digital tools in India support learning Algebra and Square Root of 1.2?
9.Does learning Algebra support future career opportunities for students in India?
Important Glossaries for the Square Root of 1.2
- Square root: The square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 4 is 2 because 2 × 2 = 4.
- Irrational number: An irrational number cannot be expressed as a simple fraction. Its decimal goes on forever without repeating.
- Principal square root: The principal square root is the non-negative square root of a number. For example, the principal square root of 9 is 3.
- Decimal: A decimal is a number that consists of a whole number and a fractional part separated by a dot, such as 1.2.
- Approximation: An approximation is a value or number that is close to the actual value but not exact. It is often used in place of a precise calculation.
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Jaskaran Singh Saluja
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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.
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