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Square Root of 656

The square root of 656 is expressed as √656 in the radical form and as (656)^½ or (656)^0.5 in the exponent form. The square root of 656 rounded up to 6 decimal places is 25.612497. It is the positive solution of the equation x² = 656. We can express the square root of 656 in its lowest radical form as 4 √41.

Square Root of 656: 25.612496949731394
Square Root of 656 in exponential form: (656)^½ or (656)^0.5
Square Root of 656 in radical form: √656 or 4 √41

Square Root of 656

1.	What is the Square Root of 656?
2.	How to find the Square Root of 656?
3.	Is the Square Root of 656 Irrational?
4.	FAQs

What is the Square Root of 656?

The square root of 656, (or root 656), is the number which when multiplied by itself gives the product as 656. Therefore, the square root of 656 = √656 = 4 √41 = 25.612496949731394.

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How to Find Square Root of 656?

Square Root of 656 by Long Division Method

Value of √656 by Long Division Method

Explanation:

Forming pairs: 06 and 56
Find a number Y (2) such that whose square is <= 6. Now divide 06 by 2 with quotient as 2.
Bring down the next pair 56, to the right of the remainder 2. The new dividend is now 256.
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 5) such that 4Z × Z <= 256. After finding Z, together 4 and Z (5) form a new divisor 45 for the new dividend 256.
Divide 256 by 45 with the quotient as 5, giving the remainder = 256 - 45 × 5 = 256 - 225 = 31.
Now, let's find the decimal places after the quotient 25.
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. 5 + 45 = 50. To the right of 50, find a digit Z (which is 6) such that 50Z × Z <= 3100. Together they form a new divisor (506) for the new dividend (3100).
Divide 3100 by 506 with the quotient as 6, giving the remainder = 3100 - 506 × 6 = 3100 - 3036 = 64.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 656.

Therefore, the square root of 656 by long division method is 25.6 approximately.

Is Square Root of 656 Irrational?

The actual value of √656 is undetermined. The value of √656 up to 25 decimal places is 25.61249694973139474595287. Hence, the square root of 656 is an irrational number.

☛ Also Check:

Square Root of 90 - √90 = 9.48683
Square Root of 85 - √85 = 9.21954
Square Root of 17 - √17 = 4.12311
Square Root of 105 - √105 = 10.24695
Square Root of 1000 - √1000 = 31.62278
Square Root of 39 - √39 = 6.24500
Square Root of 97 - √97 = 9.84886

Square Root of 656 Solved Examples

Example 1: Solve the equation x² − 656 = 0

Solution:

x² - 656 = 0 i.e. x² = 656
x = ±√656
Since the value of the square root of 656 is 25.612,
⇒ x = +√656 or -√656 = 25.612 or -25.612.
Example 2: If the area of a circle is 656π in². Find the radius of the circle.

Solution:

Let 'r' be the radius of the circle.
⇒ Area of the circle = πr² = 656π in²
⇒ r = ±√656 in
Since radius can't be negative,
⇒ r = √656
The square root of 656 is 25.612.
⇒ r = 25.612 in
Example 3: If the surface area of a sphere is 2624π in². Find the radius of the sphere.

Solution:

Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr² = 2624π in²
⇒ r = ±√656 in
Since radius can't be negative,
⇒ r = √656
The square root of 656 is 25.612.
⇒ r = 25.612 in

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FAQs on the Square Root of 656

What is the Value of the Square Root of 656?

The square root of 656 is 25.61249.

Why is the Square Root of 656 an Irrational Number?

Upon prime factorizing 656 i.e. 2⁴ × 41¹, 41 is in odd power. Therefore, the square root of 656 is irrational.

If the Square Root of 656 is 25.612. Find the Value of the Square Root of 6.56.

Let us represent √6.56 in p/q form i.e. √(656/100) = 6.56/10 = 2.561. Hence, the value of √6.56 = 2.561

What is the Square Root of 656 in Simplest Radical Form?

We need to express 656 as the product of its prime factors i.e. 656 = 2 × 2 × 2 × 2 × 41. Therefore, √656 = √2 × 2 × 2 × 2 × 41 = 4 √41. Thus, the square root of 656 in the lowest radical form is 4 √41.

Is the number 656 a Perfect Square?

The prime factorization of 656 = 2⁴ × 41¹. Here, the prime factor 41 is not in the pair. Therefore, 656 is not a perfect square.

What is the Square Root of -656?

The square root of -656 is an imaginary number. It can be written as √-656 = √-1 × √656 = i √656 = 25.612i
where i = √-1 and it is called the imaginary unit.

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