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Square Root

# What Is the Square Root of 400? | How to Find the Square Root of 400?

Written by Prerit Jain

Updated on: 17 Aug 2023

### What Is the Square Root of 400? | How to Find the Square Root of 400?

The square root of 400 is 20. The square root of 400 is found using both prime factorization and the long division method. In radical form, the square root is denoted as, and in the exponential form, they are expressed as (400)0.5  and (400)½.

The square root of 400 is either 20. The negative value is not used as -20 is not accepted for the rules of finding a square value. Hence only 20 is considered the square root of 400. When a number is multiplied by itself it gives the original value as explained or finding the square root of a number is the inversion of squaring the number.

## Methods to find the square root of 400

• Long division method
• Prime factorization method
• Repeated subtraction method

### Prime factorization

The prime factorization method is one of the simplest methods to find the square root of a number
Find the prime factors of 400
The prime factor of 400 =  2× 2×2×2 ×5×5
Group the same prime factor
By grouping the same prime factor we get 24× 52
Multiply the common prime factors

400 = 20

### Repeated subtraction

Repeated subtraction is a handy method for the ones that are not yet familiarized with prime factorization or the long division methods. The numbers that are used for subtraction are the given number and its result with only odd values. Continue the subtraction until zero is obtained. The step in which zero is obtained is the square root of the number.

1. 400 – 1 = 399
2. 399 – 3 = 396
3. 396 – 5 = 391
4. 391 – 7 = 384
5. 384 – 9 = 375
6. 375 – 11 = 364
7. 364 – 13 = 351
8. 351 – 15 = 336
9. 336 – 17 = 319
10. 319 -19 = 300
11. 300 – 21 = 279
12. 279 – 23 = 256
13. 256 – 25 = 231
14. 231 – 27 = 204
15. 204 – 29 = 175
16. 175 – 31 =144
17. 144 – 33 =11
18. 111 – 35 = 76
19. 76 – 37 = 39
20. 39 – 39 = 0

The number zero is obtained in the 20th step.
Hence, √400 = 20

### Long division

The number that is closest and can divide the dividend is chosen as the divisor.

Hence, √400 = 20

## Solved examples

Q1: Using the prime factorization method find the square root of 400.
A1: Prime factor of 400 = 2× 2×2×2 ×5×5
Hence, √400 = 20

Q2: John wants to find the square root of 400 using the long division method, let’s help him

A2: Hence, √400 = 20

Q3: The roots of – (400) and (400) are the same says Lawrence, what did you think?
A3: The negative square has no real root.
400 has real roots while  – (400) has only imaginary roots.
Hence, they are not similar

Q4: solve 2√400 + 5√400
A4:The √400 = 20
= 2 (20) + 5 (20)
= 40 + 10
Hence by solving we get 50

Q5: what is the value of x, if x√400 = 25
A5: x400 = 25
400 = 20
Hence, x 20 = 25
X = 25/20 = 5/4
Therefore x = 5/4

What is the square root of 400?
The 400 = 20.

Is 400 a rational number?
Yes, 400 is a rational number because when we divide the number we get 20 and not 0 (p/q  ≠0)

What is a perfect square number?
A perfect square number is one when we find the root of the number we get a whole number and not a decimal. 400 = 20 hence 400 is a perfect square number.

What is the square root of ℼ?
The = 1.772

Mary bought 400 saplings, and he decided to plant them with the same number in rows and columns, how could he do that?
If Mary decides to plant equal numbers in both rows and columns then he must have squared them to find how much he should plant for them to be equal.
400 = 20
Therefore, Mary planted 20 plants in each row and column.

What is the square root of 121?
The square root of 121 = 11.

How to find the square root for irrational numbers?
To find the square root for irrational numbers use the long division method

Written by by

Prerit Jain

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