A day full of math games & activities. Find one near you.

Square Root of 421

The square root of 421 is expressed as √421 in the radical form and as (421)^½ or (421)^0.5 in the exponent form. The square root of 421 rounded up to 10 decimal places is 20.5182845287. It is the positive solution of the equation x² = 421.

Square Root of 421: 20.518284528683193
Square Root of 421 in exponential form: (421)^½ or (421)^0.5
Square Root of 421 in radical form: √421

Square Root of 421

1.	What is the Square Root of 421?
2.	How to find the Square Root of 421?
3.	Is the Square Root of 421 Irrational?
4.	FAQs

What is the Square Root of 421?

The square root of 421, (or root 421), is the number which when multiplied by itself gives the product as 421. Therefore, the square root of 421 = √421 = 20.518284528683193.

☛ Check: Square Root Calculator

How to Find Square Root of 421?

Square Root of 421 by Long Division Method

Value of √421 by Long Division Method

Explanation:

Forming pairs: 04 and 21
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 21, to the right of the remainder 0. The new dividend is now 21.
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 <= 21. After finding Z, together 4 and Z (0) form a new divisor 40 for the new dividend 21.
Divide 21 by 40 with the quotient as 0, giving the remainder = 21 - 40 × 0 = 21 - 0 = 21.
Now, let's find the decimal places after the quotient 20.
Bring down 00 to the right of this remainder 21. The new dividend is now 2100.
Add the last digit of quotient to divisor i.e. 0 + 40 = 40. To the right of 40, find a digit Z (which is 5) such that 40Z × Z <= 2100. Together they form a new divisor (405) for the new dividend (2100).
Divide 2100 by 405 with the quotient as 5, giving the remainder = 2100 - 405 × 5 = 2100 - 2025 = 75.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 421.

Therefore, the square root of 421 by long division method is 20.5 approx.

Is Square Root of 421 Irrational?

The actual value of √421 is undetermined. The value of √421 up to 25 decimal places is 20.51828452868319106251974. Hence, the square root of 421 is an irrational number.

☛ Also Check:

Square Root of 97 - √97 = 9.84886
Square Root of 288 - √288 = 16.97056
Square Root of 2 - √2 = 1.41421
Square Root of 162 - √162 = 12.72792
Square Root of 22 - √22 = 4.69042
Square Root of 100 - √100 = 10
Square Root of 63 - √63 = 7.93725

Square Root of 421 Solved Examples

Example 1: Solve the equation x² − 421 = 0

Solution:

x² - 421 = 0 i.e. x² = 421
x = ±√421
Since the value of the square root of 421 is 20.518,
⇒ x = +√421 or -√421 = 20.518 or -20.518.
Example 2: If the area of a circle is 421π in². Find the radius of the circle.

Solution:

Let 'r' be the radius of the circle.
⇒ Area of the circle = πr² = 421π in²
⇒ r = ±√421 in
Since radius can't be negative,
⇒ r = √421
The square root of 421 is 20.518.
⇒ r = 20.518 in
Example 3: If the surface area of a sphere is 1684π in². Find the radius of the sphere.

Solution:

Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr² = 1684π in²
⇒ r = ±√421 in
Since radius can't be negative,
⇒ r = √421
The square root of 421 is 20.518.
⇒ r = 20.518 in

go to slide go to slide go to slide

Ready to see the world through math’s eyes?

Math is at the core of everything we do. Enjoy solving real-world math problems in live classes and become an expert at everything.

Book a Free Trial Class

FAQs on the Square Root of 421

What is the Value of the Square Root of 421?

The square root of 421 is 20.51828.

Why is the Square Root of 421 an Irrational Number?

The number 421 is prime. This implies that the number 421 is pairless and is not in the power of 2. Therefore, the square root of 421 is irrational.

What is the Square Root of -421?

The square root of -421 is an imaginary number. It can be written as √-421 = √-1 × √421 = i √421 = 20.518i
where i = √-1 and it is called the imaginary unit.

What is the Square Root of 421 in Simplest Radical Form?

The number 421 is a prime number. This implies that the number 421 is pairless and is not in the power of 2. Therefore, the radical form of square root of 421 cannot be simplified further.

What is the Square of the Square Root of 421?

The square of the square root of 421 is the number 421 itself i.e. (√421)² = (421)^2/2 = 421.

If the Square Root of 421 is 20.518. Find the Value of the Square Root of 4.21.

Let us represent √4.21 in p/q form i.e. √(421/100) = 4.21/10 = 2.052. Hence, the value of √4.21 = 2.052

Math worksheets and
visual curriculum