118 LearnersLast updated on May 26th, 2025
Square Root of 1602
If a number is multiplied by itself, the result is a square. The inverse of the square is a square root. The square root is used in various fields such as vehicle design, finance, etc. Here, we will discuss the square root of 1602.
What is the Square Root of 1602?
The square root is the inverse operation of squaring a number. 1602 is not a perfect square. The square root of 1602 is expressed in both radical and exponential form. In radical form, it is expressed as √1602, whereas (1602)^(1/2) in exponential form. √1602 ≈ 40.0225, 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 1602
The prime factorization method is used for perfect square numbers. However, for non-perfect square numbers, 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 1602 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Let us break down 1602 into its prime factors:
Step 1: Finding the prime factors of 1602 Breaking it down, we get 2 x 3 x 3 x 89: 2 x 3^2 x 89
Step 2: Now we found the prime factors of 1602. Since 1602 is not a perfect square, the digits of the number can’t be grouped into pairs.
Therefore, calculating √1602 using prime factorization alone is not feasible.
Square Root of 1602 by Long Division Method
The long division method is used for non-perfect square numbers. This method involves finding the closest perfect square number for the given number and using division to find the square root step by step.
Step 1: Begin by grouping the digits of 1602. Group it as 16 and 02.
Step 2: Find n whose square is less than or equal to 16. n is 4 since 4^2 = 16. The quotient is 4, and the remainder is 0.
Step 3: Bring down the next pair, 02, making the new dividend 02.
Step 4: Double the quotient (4) to get 8, which becomes part of the new divisor.
Step 5: Find the largest digit x such that 8x * x ≤ 02. Since 8 * 0 * 0 = 0 ≤ 02, x is 0.
Step 6: Subtract 0 from 02. The result is 02, and the quotient is 40.
Step 7: Add a decimal point and bring down two zeros. The new dividend is 200.
Step 8: Find the new divisor, which is 80. Find x such that 80x * x is less than or equal to 200. x is 2.
Step 9: Subtract 160 from 200, leaving a remainder of 40.
Step 10: Continue these steps until the desired decimal accuracy is achieved.
The square root of 1602 is approximately 40.0225.
Square Root of 1602 by Approximation Method
The approximation method is a straightforward way to estimate square roots. Let's find the square root of 1602 using this method.
Step 1: Find the closest perfect squares to √1602.
The closest perfect squares are 1600 and 1681.
√1602 falls between 40 and 41.
Step 2: Use interpolation to find a more accurate value.
(Given number - smallest perfect square) / (larger perfect square - smaller perfect square).
(1602 - 1600) / (1681 - 1600) = 2 / 81 ≈ 0.0247
Adding this to the lower bound: 40 + 0.0247 ≈ 40.0247
Thus, the square root of 1602 is approximately 40.0247.
Common Mistakes and How to Avoid Them in the Square Root of 1602
Students often make mistakes while finding square roots, such as forgetting about the negative square root or skipping steps in the long division method. Let's look at a few common mistakes in detail.
Mistake 1
Forgetting about the negative square root
It's important to remember that a number has both positive and negative square roots. However, we often focus on the positive square root in practical applications.
For example, √50 = 7.07, and there's also -7.07, which should not be forgotten.
Square Root of 1602 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √1602?
The area of the square is 1602 square units.
Explanation
The area of a square is side². The side length is given as √1602. Area of the square = (√1602)² = 1602. Therefore, the area of the square box is 1602 square units.
Problem 2
A square-shaped building measuring 1602 square feet is built; if each of the sides is √1602, what will be the square feet of half of the building?
801 square feet
Explanation
Since the building is square-shaped, we can divide the given area by 2. Dividing 1602 by 2 = 801. So, half of the building measures 801 square feet.
Problem 3
Calculate √1602 × 5.
200.1125
Explanation
The first step is to find the square root of 1602, which is approximately 40.0225. Multiply 40.0225 by 5. So, 40.0225 × 5 = 200.1125.
Problem 4
What will be the square root of (1600 + 2)?
The square root is approximately 40.0247.
Explanation
To find the square root, calculate the sum of (1600 + 2) = 1602. The square root of 1602 is approximately 40.0247. Therefore, the square root of (1600 + 2) is approximately 40.0247.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √1602 units and the width ‘w’ is 38 units.
The perimeter of the rectangle is approximately 156.045 units.
Explanation
Perimeter of the rectangle = 2 × (length + width) Perimeter = 2 × (√1602 + 38) ≈ 2 × (40.0225 + 38) ≈ 2 × 78.0225 ≈ 156.045 units.
FAQ on Square Root of 1602
1.What is √1602 in its simplest form?
2.Mention the factors of 1602.
3.Calculate the square of 1602.
4.Is 1602 a prime number?
5.1602 is divisible by?
Important Glossaries for the Square Root of 1602
- Square root: A square root is the inverse of squaring a number. For example, 4^2 = 16, and the inverse is √16 = 4.
- Irrational number: An irrational number cannot be expressed as a fraction p/q, where p and q are integers and q ≠ 0.
- Perfect square: A number is a perfect square if it is the square of an integer. For example, 144 is a perfect square because 12^2 = 144.
- Decimal: A decimal number has a whole number and a fractional part separated by a decimal point. Examples include 7.86, 8.65, and 9.42.
- Interpolation: Interpolation is a method of estimating unknown values that fall between known values.
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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
: He loves to play the quiz with kids through algebra to make kids love it.
