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Square Root of 486

The square root of 486 is expressed as √486 in the radical form and as (486)^½ or (486)^0.5 in the exponent form. The square root of 486 rounded up to 8 decimal places is 22.04540769. It is the positive solution of the equation x² = 486. We can express the square root of 486 in its lowest radical form as 9 √6.

Square Root of 486: 22.045407685048602
Square Root of 486 in exponential form: (486)^½ or (486)^0.5
Square Root of 486 in radical form: √486 or 9 √6

Square Root of 486

1.	What is the Square Root of 486?
2.	How to find the Square Root of 486?
3.	Is the Square Root of 486 Irrational?
4.	FAQs

What is the Square Root of 486?

The square root of 486, (or root 486), is the number which when multiplied by itself gives the product as 486. Therefore, the square root of 486 = √486 = 9 √6 = 22.045407685048602.

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How to Find Square Root of 486?

Square Root of 486 by Long Division Method

Value of √486 by Long Division Method

Explanation:

Forming pairs: 04 and 86
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 86, to the right of the remainder 0. The new dividend is now 86.
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 2) such that 4Z × Z <= 86. After finding Z, together 4 and Z (2) form a new divisor 42 for the new dividend 86.
Divide 86 by 42 with the quotient as 2, giving the remainder = 86 - 42 × 2 = 86 - 84 = 2.
Now, let's find the decimal places after the quotient 22.
Bring down 00 to the right of this remainder 2. The new dividend is now 200.
Add the last digit of quotient to divisor i.e. 2 + 42 = 44. To the right of 44, find a digit Z (which is 0) such that 44Z × Z <= 200. Together they form a new divisor (440) for the new dividend (200).
Divide 200 by 440 with the quotient as 0, giving the remainder = 200 - 440 × 0 = 200 - 0 = 200.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 486.

Therefore, the square root of 486 by long division method is 22.0 approx.

Is Square Root of 486 Irrational?

The actual value of √486 is undetermined. The value of √486 up to 25 decimal places is 22.04540768504860288377556. Hence, the square root of 486 is an irrational number.

☛ Also Check:

Square Root of 21 - √21 = 4.58258
Square Root of 109 - √109 = 10.44031
Square Root of 25 - √25 = 5
Square Root of 23 - √23 = 4.79583
Square Root of 240 - √240 = 15.49193
Square Root of 136 - √136 = 11.66190
Square Root of 74 - √74 = 8.60233

Square Root of 486 Solved Examples

Example 1: Solve the equation x² − 486 = 0

Solution:

x² - 486 = 0 i.e. x² = 486
x = ±√486
Since the value of the square root of 486 is 22.045,
⇒ x = +√486 or -√486 = 22.045 or -22.045.
Example 2: If the surface area of a cube is 2916 in². Find the length of the side of the cube.

Solution:

Let 'a' be the length of the side of the cube.
⇒ Area of the cube = 6a² = 2916 in²
⇒ a = ±√486 in
Since length can't be negative,
⇒ a = √486
We know that the square root of 486 is 22.045.
⇒ a = 22.045 in
Example 3: If the surface area of a sphere is 1944π in². Find the radius of the sphere.

Solution:

Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr² = 1944π in²
⇒ r = ±√486 in
Since radius can't be negative,
⇒ r = √486
The square root of 486 is 22.045.
⇒ r = 22.045 in

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FAQs on the Square Root of 486

What is the Value of the Square Root of 486?

The square root of 486 is 22.0454.

Why is the Square Root of 486 an Irrational Number?

Upon prime factorizing 486 i.e. 2¹ × 3⁵, 2 is in odd power. Therefore, the square root of 486 is irrational.

Is the number 486 a Perfect Square?

The prime factorization of 486 = 2¹ × 3⁵. Here, the prime factor 2 is not in the pair. Therefore, 486 is not a perfect square.

Evaluate 8 plus 7 square root 486

The given expression is 8 + 7 √486. We know that the square root of 486 is 22.045. Therefore, 8 + 7 √486 = 8 + 7 × 22.045 = 8 + 154.318 = 162.318

What is the Square Root of 486 in Simplest Radical Form?

We need to express 486 as the product of its prime factors i.e. 486 = 2 × 3 × 3 × 3 × 3 × 3. Therefore, √486 = √2 × 3 × 3 × 3 × 3 × 3 = 9 √6. Thus, the square root of 486 in the lowest radical form is 9 √6.

What is the Value of 15 square root 486?

The square root of 486 is 22.045. Therefore, 15 √486 = 15 × 22.045 = 330.681.

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