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625 LearnersLast updated on August 5, 2025
Square Root of 1.6
What is the Square Root of 1.6?
The square root is the inverse of the square of the number. 1.6 is not a perfect square. The square root of 1.6 is expressed in both radical and exponential form. In the radical form, it is expressed as √1.6, whereas (1.6)^(1/2) in the exponential form. √1.6 ≈ 1.26491, 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 1.6
The prime factorization method is typically used for perfect square numbers. However, for non-perfect square numbers like 1.6, the long division method and approximation method are used. Let us now learn the following methods:
- Long division method
- Approximation method
Square Root of 1.6 by Long Division Method
The long division method is particularly used for non-perfect square numbers. This method involves finding the square root step by step. Let us now learn how to find the square root of 1.6 using the long division method:
Step 1: Begin by pairing digits from right to left. In the case of 1.6, consider it as 1.6000 to facilitate the division.
Step 2: Find a number whose square is less than or equal to 1. The number is 1, because 1 × 1 = 1.
Step 3: Subtract 1 from 1, the remainder is 0. Bring down the next pair of digits, which is 60.
Step 4: Double the divisor (1), which gives 2, and use it as the new divisor. Set the next digit of the quotient as n so that 2n × n ≤ 60.
Step 5: Determine n by trial and error. Here, n is 2, because 22 × 2 = 44.
Step 6: Subtract 44 from 60, the remainder is 16. Bring down the next pair of digits, making it 1600.
Step 7: Double the current quotient (12) to get 24, and use it as the new divisor. Determine n such that 24n × n ≤ 1600. Here, n is 6, because 246 × 6 = 1476.
Step 8: Subtract 1476 from 1600, leaving a remainder of 124.
Step 9: Continue this process to achieve the desired precision.
The approximate square root of 1.6 is 1.26491.
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Square Root of 1.6 by Approximation Method
The approximation method is a simple way to find the square root of a given number. Here’s how to find the square root of 1.6 using this method:
Step 1: Identify the perfect squares closest to 1.6. The smallest perfect square less than 1.6 is 1 (√1 = 1) and the largest perfect square greater than 1.6 is 4 (√4 = 2).
Step 2: Recognize that √1.6 is between 1 and 2.
Step 3: Use interpolation to approximate. The value of √1.6 is closer to 1 than to 2. A rough estimate gives √1.6 ≈ 1.26491.
Common Mistakes and How to Avoid Them in the Square Root of 1.6
Students often make mistakes while finding the square root, such as forgetting about the negative square root, skipping long division steps, etc. Let us look at a few common mistakes in detail.
Mistake 1
Forgetting about the negative square root
It is important to remember that a number has both positive and negative square roots. However, we typically consider only the positive square root, as it is used more often.
For example, √1.6 ≈ 1.26491, but there is also -1.26491.
Mistake 2
Not adding square root symbol in proper places
Not using the square root symbol properly is a common mistake. It is crucial to simplify expressions inside the square root before proceeding.
For example, √(1 + 0.6) is not equal to √1 + √0.6.
Mistake 3
Not finding the correct value of a non-perfect square
Ensure students simplify numbers inside the square root to avoid errors in identifying approximate values.
For example, √1.6 ≈ 1.26491, but incorrectly estimating √1.6 as 1.25 is a mistake.
Mistake 5
Making mistakes in long division
Finding a square root using the long division method involves many steps, and students may accidentally skip a step, leading to incorrect results. This could occur during subtraction or elsewhere.
Square Root of 1.6 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √1.8?
The area of the square is 3.24 square units.
Explanation
The area of the square = side².
The side length is given as √1.8.
Area of the square = (√1.8)² = 1.8.
Therefore, the area of the square box is 3.24 square units.
Problem 2
A square-shaped plot measuring 1.6 square meters is built. If each of the sides is √1.6, what will be the square meters of half of the plot?
0.8 square meters
Explanation
We can divide the given area by 2 as the plot is square-shaped.
Dividing 1.6 by 2, we get 0.8.
So half of the plot measures 0.8 square meters.
Problem 3
Calculate √1.6 × 5.
6.32455
Explanation
First, find the square root of 1.6, which is approximately 1.26491.
Then multiply 1.26491 by 5. So, 1.26491 × 5 ≈ 6.32455.
Problem 4
What will be the square root of (1.4 + 0.2)?
The square root is 1.2.
Explanation
Find the sum of (1.4 + 0.2), which equals 1.6.
Therefore, the square root of 1.6 is approximately ±1.26491.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √1.8 units and the width ‘w’ is 3.8 units.
The perimeter of the rectangle is approximately 10.528 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√1.8 + 3.8)
≈ 2 × (1.34 + 3.8)
≈ 10.528 units.
FAQ on Square Root of 1.6
1.What is √1.6 in its simplest form?
2.Is 1.6 a perfect square?
3.Calculate the square of 1.6.
4.Is 1.6 a rational number?
5.What is the approximate value of √1.6?
Important Glossaries for the Square Root of 1.6
- Square root: The square root of a number is a value that, when multiplied by itself, gives the original number. Example: √4 = 2.
- Irrational number: An irrational number is a number that cannot be expressed as a simple fraction, such as √1.6.
- Approximation: Approximation is estimating a number to a near value, often used for non-perfect squares like √1.6.
- Long division method: A technique used to find the square root of non-perfect squares by a step-by-step division process.
- Perfect square: A number that is the square of an integer. Example: 4 is a perfect square because 2 × 2 = 4.
Vikrant Sharma
About the Author
Vikrant Sharma 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.
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