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Square Root of 420

The square root of 420 is expressed as √420 in the radical form and as (420)^½ or (420)^0.5 in the exponent form. The square root of 420 rounded up to 9 decimal places is 20.493901532. It is the positive solution of the equation x² = 420. We can express the square root of 420 in its lowest radical form as 2 √105.

Square Root of 420: 20.493901531919196
Square Root of 420 in exponential form: (420)^½ or (420)^0.5
Square Root of 420 in radical form: √420 or 2 √105

Square Root of 420

1.	What is the Square Root of 420?
2.	How to find the Square Root of 420?
3.	Is the Square Root of 420 Irrational?
4.	FAQs

What is the Square Root of 420?

The square root of 420, (or root 420), is the number which when multiplied by itself gives the product as 420. Therefore, the square root of 420 = √420 = 2 √105 = 20.493901531919196.

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How to Find Square Root of 420?

Square Root of 420 by Long Division Method

Value of √420 by Long Division Method

Explanation:

Forming pairs: 04 and 20
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 20, to the right of the remainder 0. The new dividend is now 20.
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 <= 20. After finding Z, together 4 and Z (0) form a new divisor 40 for the new dividend 20.
Divide 20 by 40 with the quotient as 0, giving the remainder = 20 - 40 × 0 = 20 - 0 = 20.
Now, let's find the decimal places after the quotient 20.
Bring down 00 to the right of this remainder 20. The new dividend is now 2000.
Add the last digit of quotient to divisor i.e. 0 + 40 = 40. To the right of 40, find a digit Z (which is 4) such that 40Z × Z <= 2000. Together they form a new divisor (404) for the new dividend (2000).
Divide 2000 by 404 with the quotient as 4, giving the remainder = 2000 - 404 × 4 = 2000 - 1616 = 384.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 420.

Therefore, the square root of 420 by long division method is 20.4 approximately.

Is Square Root of 420 Irrational?

The actual value of √420 is undetermined. The value of √420 up to 25 decimal places is 20.49390153191919676644208. Hence, the square root of 420 is an irrational number.

☛ Also Check:

Square Root of 75 - √75 = 8.66025
Square Root of 49 - √49 = 7
Square Root of 1521 - √1521 = 39
Square Root of 22 - √22 = 4.69042
Square Root of 77 - √77 = 8.77496
Square Root of 140 - √140 = 11.83216
Square Root of 225 - √225 = 15

Square Root of 420 Solved Examples

Example 1: Solve the equation x² − 420 = 0

Solution:

x² - 420 = 0 i.e. x² = 420
x = ±√420
Since the value of the square root of 420 is 20.494,
⇒ x = +√420 or -√420 = 20.494 or -20.494.
Example 2: If the surface area of a sphere is 1680π in². Find the radius of the sphere.

Solution:

Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr² = 1680π in²
⇒ r = ±√420 in
Since radius can't be negative,
⇒ r = √420
The square root of 420 is 20.494.
⇒ r = 20.494 in
Example 3: If the area of an equilateral triangle is 420√3 in². Find the length of one of the sides of the triangle.

Solution:

Let 'a' be the length of one of the sides of the equilateral triangle.
⇒ Area of the equilateral triangle = (√3/4)a² = 420√3 in²
⇒ a = ±√1680 in
Since length can't be negative,
⇒ a = √1680 = 2 √420
We know that the square root of 420 is 20.494.
⇒ a = 40.988 in

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FAQs on the Square Root of 420

What is the Value of the Square Root of 420?

The square root of 420 is 20.4939.

Why is the Square Root of 420 an Irrational Number?

Upon prime factorizing 420 i.e. 2² × 3¹ × 5¹ × 7¹, 3 is in odd power. Therefore, the square root of 420 is irrational.

What is the Square Root of -420?

The square root of -420 is an imaginary number. It can be written as √-420 = √-1 × √420 = i √420 = 20.493i
where i = √-1 and it is called the imaginary unit.

What is the Square of the Square Root of 420?

The square of the square root of 420 is the number 420 itself i.e. (√420)² = (420)^2/2 = 420.

Is the number 420 a Perfect Square?

The prime factorization of 420 = 2² × 3¹ × 5¹ × 7¹. Here, the prime factor 3 is not in the pair. Therefore, 420 is not a perfect square.

If the Square Root of 420 is 20.494. Find the Value of the Square Root of 4.2.

Let us represent √4.2 in p/q form i.e. √(420/100) = 4.2/10 = 2.049. Hence, the value of √4.2 = 2.049

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