Table Of Contents
220 LearnersLast updated on December 2nd, 2024
Square root of 1600
Let’s discuss what is a square root? The square root of a number is a number, when multiplied by itself gives the number. Radical symbol (√) is the symbol used to indicate square root. The square root of 25 is ±5. We use it in our daily life in physics, engineering, finance etc.
What is the square root of 1600
In this topic, the square root of 1600 is ±40. The square root of 1600 is expressed as √1600, in radical form. It is expressed as (1600)½ in exponential form.
Finding the square root of 1600
If a student wants to find the square root of a number. Which are the methods they can use? Some common methods are,
- Prime factorization
- Long division
- Approximation
- Subtraction method
Let’s check the square root of 1600 using these methods
Square root of 1600 by prime factorization
In this method, all the prime factors of the number are listed down and then from there one number from each pair is listed down. Then the numbers are multiplied together.
By using prime factorization, let’s check out the square root of 1600.
Step 1: Listing out the prime factors of 1600 and pairing the same numbers.
Prime factors of 1600 = 2 × 2 × 2 × 2 × 2 × 2 × 5 × 5
Pairing the factors i.e, (2 × 2), (2 × 2), (2 × 2), (5 × 5)
Step 2: multiplying a number from each pair
2 × 2 × 2 × 5 =40
Hence, the √1600 is 40
Square root of 1600 by long division
Here, the given number is divided into smaller numbers to find the square root of the number.
Using the long division method, let’s check the square root of 1600
Step 1: finding the number whose square is less than or equal to the 1600
Here the number is 40, because 402 = 1600
Step 2: So, let’s divide 1600 by 40
Step 3: continue the process till the remainder is 0
The quotient will be the square root of the number.
Therefore, square root of 1600 is 40
Square root of 1600 by approximation
Approximation method is mainly used for not a perfect square. As 1600 is a perfect square, the approximation method is not used to find the square root of 1600.
Square root of 1600 by subtraction method
In the subtraction method, based on the fact, the sum of the first n odd number is n2. So, here the given number is subtracted with the odd number starting with 1. The process will go on till the given number becomes 0. Here, the step count is equal to the square root of the number.
Step 1: The given number is subtracted from 1, i.e, 1600 - 1 = 1599
Step 2: The obtained number is subtracted with the next odd number. Here, the number is 3, so 1599 - 3 =1596.
Step 3: Continue the process till the number is 0. Here the process will continue till step 40. Hence, the square root of 1600 is ±40.
1600 - 1 =1599 → step 1
1599 - 3 =1596 → step 2
1596 - 5 =1591 → step 3
1591 - 7 =1584 → step 4
1584 - 9 =1575 → step 5
1575 - 11 =1564 → step 6
1564 - 13 =1551 → step 7
………………….…………
………………….…………
………………….…………
………………….…………
231 - 75 =156 → step 38
156 - 77=79 → step 39
79 - 79 =0 → step 40
Common errors and how to avoid them in the square root of 1600
Students tend to make errors while finding the square root of a number. So, let’s check some common errors while finding the square root and the ways to avoid it
Mistake 1
Errors while counting the prime factors
Students tend to make errors in the prime factorization method by making errors in counting. To avoid it, make sure to recount each factor. And make sure to verify the answer.
Square root of 1600 examples
Problem 1
If y = √16, find y²?
Here, y = √16
Which means y = 4
So, y2 = 4 × 4 =16
Therefore, y2 = 16
Explanation
The square of a square root will always be the number.
Problem 2
solve the following (a) √1600 + √1600 (b) √1600 x √1600?
First, let’s check √1600 + √1600,
√1600 = 40
So, √1600 +√1600
= 40 + 40
= 80
Now let’s check √1600 × √1600
As, √1600 = 40
√1600 × √1600
= 40 × 40
= 1600.
Explanation
Therefore, √1600 + √1600 = 80 and √1600 x √1600 = 1600
Problem 3
If the area of a square is 1600, what would be the length of each side?
The area of the square = s2
S2 = 1600
Therefore, the length of each side = √1600 = 40 units.
Explanation
The area of a square is s2. To find the length of a side of a square is easy once we have the area. The square root of the area is the side of a square.
Problem 4
Find the value of 4√1600
The value of √1600 = 40
4√1600
= 4 × 40
= 160
Explanation
To multiplying any number with a square root. Multiply the number with the value of the square root.
Problem 5
Find the value of 2/√1600?
The value of √1600 = 40
2 / √1600
= 2 / 40
= 1/20
Explanation
While dividing any number with a square root. We need to divide the number with the value of the square root.
FAQs on 1600 square root
1.Check whether 1600 is a perfect square or not?
2.Calculate the square root of 64?
3.Find the value of √576?
4.List out the prime factors of 1600
5.What is the value of √16?
6.Is √1600 value a rational or irrational number?
Important glossaries for square root of 1600
- Quotient: The result we got after dividing two numbers is the quotient
- Radical symbol: The radical symbol (√) is the symbol used to denote square root.
- Square of a number: The Square of a number is the product of the number when multiplied by itself.
- Prime factorization: It is the process of breaking down a number into prime numbers.
Explore More algebra
Previous to Square root of 1600
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.
