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Square Root of 468

The square root of 468 is expressed as √468 in the radical form and as (468)^½ or (468)^0.5 in the exponent form. The square root of 468 rounded up to 7 decimal places is 21.6333077. It is the positive solution of the equation x² = 468. We can express the square root of 468 in its lowest radical form as 6 √13.

Square Root of 468: 21.633307652783937
Square Root of 468 in exponential form: (468)^½ or (468)^0.5
Square Root of 468 in radical form: √468 or 6 √13

Square Root of 468

1.	What is the Square Root of 468?
2.	How to find the Square Root of 468?
3.	Is the Square Root of 468 Irrational?
4.	FAQs

What is the Square Root of 468?

The square root of 468, (or root 468), is the number which when multiplied by itself gives the product as 468. Therefore, the square root of 468 = √468 = 6 √13 = 21.633307652783937.

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How to Find Square Root of 468?

Square Root of 468 by Long Division Method

Value of √468 by Long Division Method

Explanation:

Forming pairs: 04 and 68
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 68, to the right of the remainder 0. The new dividend is now 68.
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 1) such that 4Z × Z <= 68. After finding Z, together 4 and Z (1) form a new divisor 41 for the new dividend 68.
Divide 68 by 41 with the quotient as 1, giving the remainder = 68 - 41 × 1 = 68 - 41 = 27.
Now, let's find the decimal places after the quotient 21.
Bring down 00 to the right of this remainder 27. The new dividend is now 2700.
Add the last digit of quotient to divisor i.e. 1 + 41 = 42. To the right of 42, find a digit Z (which is 6) such that 42Z × Z <= 2700. Together they form a new divisor (426) for the new dividend (2700).
Divide 2700 by 426 with the quotient as 6, giving the remainder = 2700 - 426 × 6 = 2700 - 2556 = 144.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 468.

Therefore, the square root of 468 by long division method is 21.6 approximately.

Is Square Root of 468 Irrational?

The actual value of √468 is undetermined. The value of √468 up to 25 decimal places is 21.63330765278393575871533. Hence, the square root of 468 is an irrational number.

☛ Also Check:

Square Root of 13 - √13 = 3.60555
Square Root of 73 - √73 = 8.54400
Square Root of 200 - √200 = 14.14214
Square Root of 325 - √325 = 18.02776
Square Root of 28 - √28 = 5.29150
Square Root of 108 - √108 = 10.39230
Square Root of 48 - √48 = 6.92820

Square Root of 468 Solved Examples

Example 1: Solve the equation x² − 468 = 0

Solution:

x² - 468 = 0 i.e. x² = 468
x = ±√468
Since the value of the square root of 468 is 21.633,
⇒ x = +√468 or -√468 = 21.633 or -21.633.
Example 2: If the area of a circle is 468π in². Find the radius of the circle.

Solution:

Let 'r' be the radius of the circle.
⇒ Area of the circle = πr² = 468π in²
⇒ r = ±√468 in
Since radius can't be negative,
⇒ r = √468
The square root of 468 is 21.633.
⇒ r = 21.633 in
Example 3: If the area of a square is 468 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 = 468 in²
⇒ a = ±√468 in
Since length can't be negative,
⇒ a = √468 = 21.633 in

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FAQs on the Square Root of 468

What is the Value of the Square Root of 468?

The square root of 468 is 21.6333.

Why is the Square Root of 468 an Irrational Number?

Upon prime factorizing 468 i.e. 2² × 3² × 13¹, 13 is in odd power. Therefore, the square root of 468 is irrational.

What is the Square of the Square Root of 468?

The square of the square root of 468 is the number 468 itself i.e. (√468)² = (468)^2/2 = 468.

What is the Square Root of -468?

The square root of -468 is an imaginary number. It can be written as √-468 = √-1 × √468 = i √468 = 21.633i
where i = √-1 and it is called the imaginary unit.

Is the number 468 a Perfect Square?

The prime factorization of 468 = 2² × 3² × 13¹. Here, the prime factor 13 is not in the pair. Therefore, 468 is not a perfect square.

What is the Value of 5 square root 468?

The square root of 468 is 21.633. Therefore, 5 √468 = 5 × 21.633 = 108.167.

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