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.

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

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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

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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Value of √656 by Long Division Method

Explanation:

Forming pairs: 06 and 56Find a number Y (2) such that whose square is 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 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 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.


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.

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Example 1: Solve the equation x2 − 656 = 0

Solution:

x2 - 656 = 0 i.e. x2 = 656x = ±√656Since 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 inSince radius can't be negative,⇒ r = √656The 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.

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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 = 25.612iwhere i = √-1 and it is called the imaginary unit.