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Square Root of 431

The square root of 431 is expressed as √431 in the radical form and as (431)^½ or (431)^0.5 in the exponent form. The square root of 431 rounded up to 8 decimal places is 20.76053949. It is the positive solution of the equation x² = 431.

Square Root of 431: 20.760539492026695
Square Root of 431 in exponential form: (431)^½ or (431)^0.5
Square Root of 431 in radical form: √431

Square Root of 431

1.	What is the Square Root of 431?
2.	How to find the Square Root of 431?
3.	Is the Square Root of 431 Irrational?
4.	FAQs

What is the Square Root of 431?

The square root of 431, (or root 431), is the number which when multiplied by itself gives the product as 431. Therefore, the square root of 431 = √431 = 20.760539492026695.

☛ Check: Square Root Calculator

How to Find Square Root of 431?

Square Root of 431 by Long Division Method

Value of √431 by Long Division Method

Explanation:

Forming pairs: 04 and 31
Find a number Y (2) such that whose square is <= 4. Now divide 04 by 2 with quotient as 2.
Bring down the next pair 31, to the right of the remainder 0. The new dividend is now 31.
Add the last digit of the quotient (2) to the divisor (2) i.e. 2 + 2 = 4. To the right of 4, find a digit Z (which is 0) such that 4Z × Z <= 31. After finding Z, together 4 and Z (0) form a new divisor 40 for the new dividend 31.
Divide 31 by 40 with the quotient as 0, giving the remainder = 31 - 40 × 0 = 31 - 0 = 31.
Now, let's find the decimal places after the quotient 20.
Bring down 00 to the right of this remainder 31. The new dividend is now 3100.
Add the last digit of quotient to divisor i.e. 0 + 40 = 40. To the right of 40, find a digit Z (which is 7) such that 40Z × Z <= 3100. Together they form a new divisor (407) for the new dividend (3100).
Divide 3100 by 407 with the quotient as 7, giving the remainder = 3100 - 407 × 7 = 3100 - 2849 = 251.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 431.

Therefore, the square root of 431 by long division method is 20.7 approx.

Is Square Root of 431 Irrational?

The actual value of √431 is undetermined. The value of √431 up to 25 decimal places is 20.76053949202669443962250. Hence, the square root of 431 is an irrational number.

☛ Also Check:

Square Root of 34 - √34 = 5.83095
Square Root of 11 - √11 = 3.31662
Square Root of 1000 - √1000 = 31.62278
Square Root of 729 - √729 = 27
Square Root of 1024 - √1024 = 32
Square Root of 16 - √16 = 4
Square Root of 63 - √63 = 7.93725

Square Root of 431 Solved Examples

Example 1: Solve the equation x² − 431 = 0

Solution:

x² - 431 = 0 i.e. x² = 431
x = ±√431
Since the value of the square root of 431 is 20.761,
⇒ x = +√431 or -√431 = 20.761 or -20.761.
Example 2: If the area of a square is 431 in². Find the length of the side of the square.

Solution:

Let 'a' be the length of the side of the square.
⇒ Area of the square = a² = 431 in²
⇒ a = ±√431 in
Since length can't be negative,
⇒ a = √431 = 20.761 in
Example 3: If the area of a circle is 431π in². Find the radius of the circle.

Solution:

Let 'r' be the radius of the circle.
⇒ Area of the circle = πr² = 431π in²
⇒ r = ±√431 in
Since radius can't be negative,
⇒ r = √431
The square root of 431 is 20.761.
⇒ r = 20.761 in

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FAQs on the Square Root of 431

What is the Value of the Square Root of 431?

The square root of 431 is 20.76053.

Why is the Square Root of 431 an Irrational Number?

The number 431 is prime. This implies that the number 431 is pairless and is not in the power of 2. Therefore, the square root of 431 is irrational.

What is the Square Root of -431?

The square root of -431 is an imaginary number. It can be written as √-431 = √-1 × √431 = i √431 = 20.76i
where i = √-1 and it is called the imaginary unit.

What is the Square Root of 431 in Simplest Radical Form?

The number 431 is a prime number. This implies that the number 431 is pairless and is not in the power of 2. Therefore, the radical form of square root of 431 cannot be simplified further.

Evaluate 4 plus 20 square root 431

The given expression is 4 + 20 √431. We know that the square root of 431 is 20.761. Therefore, 4 + 20 √431 = 4 + 20 × 20.761 = 4 + 415.211 = 419.211

What is the Value of 12 square root 431?

The square root of 431 is 20.761. Therefore, 12 √431 = 12 × 20.761 = 249.126.

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