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Square Root of 628

The square root of 628 is expressed as √628 in the radical form and as (628)^½ or (628)^0.5 in the exponent form. The square root of 628 rounded up to 6 decimal places is 25.059928. It is the positive solution of the equation x² = 628. We can express the square root of 628 in its lowest radical form as 2 √157.

Square Root of 628: 25.059928172283335
Square Root of 628 in exponential form: (628)^½ or (628)^0.5
Square Root of 628 in radical form: √628 or 2 √157

Square Root of 628

1.	What is the Square Root of 628?
2.	How to find the Square Root of 628?
3.	Is the Square Root of 628 Irrational?
4.	FAQs

What is the Square Root of 628?

The square root of 628, (or root 628), is the number which when multiplied by itself gives the product as 628. Therefore, the square root of 628 = √628 = 2 √157 = 25.059928172283335.

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How to Find Square Root of 628?

Square Root of 628 by Long Division Method

Value of √628 by Long Division Method

Explanation:

Forming pairs: 06 and 28
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 28, to the right of the remainder 2. The new dividend is now 228.
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 <= 228. After finding Z, together 4 and Z (5) form a new divisor 45 for the new dividend 228.
Divide 228 by 45 with the quotient as 5, giving the remainder = 228 - 45 × 5 = 228 - 225 = 3.
Now, let's find the decimal places after the quotient 25.
Bring down 00 to the right of this remainder 3. The new dividend is now 300.
Add the last digit of quotient to divisor i.e. 5 + 45 = 50. To the right of 50, find a digit Z (which is 0) such that 50Z × Z <= 300. Together they form a new divisor (500) for the new dividend (300).
Divide 300 by 500 with the quotient as 0, giving the remainder = 300 - 500 × 0 = 300 - 0 = 300.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 628.

Therefore, the square root of 628 by long division method is 25.0 approximately.

Is Square Root of 628 Irrational?

The actual value of √628 is undetermined. The value of √628 up to 25 decimal places is 25.05992817228333557699073. Hence, the square root of 628 is an irrational number.

☛ Also Check:

Square Root of 1681 - √1681 = 41
Square Root of 44 - √44 = 6.63325
Square Root of 99 - √99 = 9.94987
Square Root of 75 - √75 = 8.66025
Square Root of 30 - √30 = 5.47723
Square Root of 289 - √289 = 17
Square Root of 140 - √140 = 11.83216

Square Root of 628 Solved Examples

Example 1: Solve the equation x² − 628 = 0

Solution:

x² - 628 = 0 i.e. x² = 628
x = ±√628
Since the value of the square root of 628 is 25.060,
⇒ x = +√628 or -√628 = 25.060 or -25.060.
Example 2: If the area of a square is 628 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 = 628 in²
⇒ a = ±√628 in
Since length can't be negative,
⇒ a = √628 = 25.060 in
Example 3: If the area of an equilateral triangle is 628√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 = 628√3 in²
⇒ a = ±√2512 in
Since length can't be negative,
⇒ a = √2512 = 2 √628
We know that the square root of 628 is 25.060.
⇒ a = 50.120 in

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FAQs on the Square Root of 628

What is the Value of the Square Root of 628?

The square root of 628 is 25.05992.

Why is the Square Root of 628 an Irrational Number?

Upon prime factorizing 628 i.e. 2² × 157¹, 157 is in odd power. Therefore, the square root of 628 is irrational.

If the Square Root of 628 is 25.060. Find the Value of the Square Root of 6.28.

Let us represent √6.28 in p/q form i.e. √(628/100) = 6.28/10 = 2.506. Hence, the value of √6.28 = 2.506

Is the number 628 a Perfect Square?

The prime factorization of 628 = 2² × 157¹. Here, the prime factor 157 is not in the pair. Therefore, 628 is not a perfect square.

What is the Value of 6 square root 628?

The square root of 628 is 25.060. Therefore, 6 √628 = 6 × 25.060 = 150.360.

What is the Square of the Square Root of 628?

The square of the square root of 628 is the number 628 itself i.e. (√628)² = (628)^2/2 = 628.

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