Square Root of 1600
The square root of a number is the number, that gives the original number on squaring. Let us talk about the number 1600, it is an even composite number. In this lesson, you will learn the square root of 1600 and how to find square root of 1600. Did you know that 1600 is a perfect square number? When the square root of 1600 is calculated, we will obtain an answer which is a rational number. Let us learn how to calculate the square root of 1600 by long division method and by prime factorization method. We will also go through some solved examples and interactive questions. The square root of 1600 is:
 Square Root of 1600:√1600 = 40
 Square of 1600: 1600² = 2560000
1.  What Is the Square Root of 1600? 
2.  Is Square Root of 1600 Rational or Irrational? 
3.  How to Find the Square Root of 1600? 
4.  FAQs on Square Root of 1600 
What Is the Square Root of 1600?
The square root of a number is a value that on square gives the original number. The square root of 1600 is denoted by √1600 can be easily calculated by observation such as let us take example of a square root of 16 i.e. 4 and square root of 100 i.e., 10. Combining both the numbers we have 40 as a resultant number. Hence, the square root of 1600 is 40.
You can remember it this way: When the square moves from one side to the other side of the equation, it becomes the square root. 40^{2 }= 1600 ⇒ √1600 = 40. Thus, the square root of 1600 is 40.
Is Square Root of 1600 Rational or Irrational?
A rational number can be expressed as a ratio of two numbers. Now we know that √1600 = 40 = 40/1, so we could express √1600 as a fraction that is in the form of p/q and hence it is a rational number.
How to Find Square Root of 1600?
We can find the square root of 1600 using various methods.
 Repeated Subtraction
 Prime Factorization
 Estimation and Approximation
 Long Division
To learn more about each of these methods, you may learn it here. Since we could find that 1600 is a perfect square, we can find its square root using the prime factorization easily.
Square Root of 1600 Using Prime Factorization
The prime factorization of 1600 can be found as 2 × 2 × 2 × 2 ×2 × 2 × 5 × 5. To find the square root of 1600, we take one number from each pair of the same numbers and we multiply them.
√1600 =√(2 × 2 × 2 × 2 ×2 × 2 × 5 × 5 ) = 2 × 2 × 2 × 5 = 40
Square Root of 1600 by Long Division
The square root of 1600 can be found using the long division as follows:
Think of a number which when multiplied by itself gives:
 a number that is less than or equal to 1600
 a number that is very close to 1600
Since the remainder is 0, we do not need to proceed with long division further and we consider the quotient (which is 40) as the result.
Explore Square roots using illustrations and interactive examples
Important Notes
 If we do not have pairs of the same numbers as above, then the prime factorization cannot be used to find the exact square root. Instead, we have to use the long division method.
 The prime factorization method is used to write a square root of a nonperfect square number in the simplest radical form.
 1600 is a number that is a perfect square which means that it has a natural number as its square root.
 Square root of 1600 is 40.
 Square root of 1600 can be expressed as a fraction in the form p/q which tells us that the square root of 1600 is a rational number.
 The square root of 1600 is either 40 or (40).
Think Tank
 Can the value of √1600 be 40 as well? Hint: Think what is (−40)^{2}.
 Is √(−1600) a real number? Think about whether there is any real number whose square is negative.
Square Root of 1600 Solved Examples

Example 1 Serena is instructed to find the square root of 1600 using the laws of exponents. Can you help her with this?
Solution
The square root can be always replaced with the exponent 1/2.
√1600= 1600^{1/2 }= (40^{2})^{1/2 }[∵ 40^{2 }= 1600] = 40
Thus, ∴ √1600 = 40 
Example 2 Alex is trying to figure out whether 1600 is a perfect square. What method can he use to find the square root of 1600 quickly?
Solution
Alex can figure out the square root of 1600 by various methods. By using the observation, we can see:
16= 4 × 4 and 100 = 10×10
Therefore,1600= 16 × 100= 4 × 4 × 10×10 =,40×40
Hence,1600 is a perfect square (√1600 = 40).
FAQs on Square Root of 1600
What is a square root of 1600?
As we learned on this page, the square root of 1600 can be either 40 or 40.
Is 1600 a perfect square?
Yes, 1600 is a perfect square. A perfect square is a number that can be expressed as the square of a number and 40 × 40 = 1600.
What is the square root of 1600 using prime factorization?
√1600 =√(2 × 2 × 2 × 2 ×2 × 2 × 5 × 5 ) = 2 × 2 × 2 × 5 = 40.
Is the square root of 1600 rational or irrational?
The square root of 1600 is a rational number because it can be expressed in p/q form.
What is the value of sum of √1600 and √1600?
The value of √1600 + √1600 = 2√1600.
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