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Square Root of 674

The square root of 674 is expressed as √674 in the radical form and as (674)^½ or (674)^0.5 in the exponent form. The square root of 674 rounded up to 7 decimal places is 25.9615100. It is the positive solution of the equation x² = 674.

Square Root of 674: 25.96150997149434
Square Root of 674 in exponential form: (674)^½ or (674)^0.5
Square Root of 674 in radical form: √674

Square Root of 674

1.	What is the Square Root of 674?
2.	How to find the Square Root of 674?
3.	Is the Square Root of 674 Irrational?
4.	FAQs

What is the Square Root of 674?

The square root of 674, (or root 674), is the number which when multiplied by itself gives the product as 674. Therefore, the square root of 674 = √674 = 25.96150997149434.

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How to Find Square Root of 674?

Square Root of 674 by Long Division Method

Value of √674 by Long Division Method

Explanation:

Forming pairs: 06 and 74
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 74, to the right of the remainder 2. The new dividend is now 274.
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 <= 274. After finding Z, together 4 and Z (5) form a new divisor 45 for the new dividend 274.
Divide 274 by 45 with the quotient as 5, giving the remainder = 274 - 45 × 5 = 274 - 225 = 49.
Now, let's find the decimal places after the quotient 25.
Bring down 00 to the right of this remainder 49. The new dividend is now 4900.
Add the last digit of quotient to divisor i.e. 5 + 45 = 50. To the right of 50, find a digit Z (which is 9) such that 50Z × Z <= 4900. Together they form a new divisor (509) for the new dividend (4900).
Divide 4900 by 509 with the quotient as 9, giving the remainder = 4900 - 509 × 9 = 4900 - 4581 = 319.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 674.

Therefore, the square root of 674 by long division method is 25.9 approx.

Is Square Root of 674 Irrational?

The actual value of √674 is undetermined. The value of √674 up to 25 decimal places is 25.96150997149433910407036. Hence, the square root of 674 is an irrational number.

☛ Also Check:

Square Root of 196 - √196 = 14
Square Root of 288 - √288 = 16.97056
Square Root of 289 - √289 = 17
Square Root of 10 - √10 = 3.16228
Square Root of 28 - √28 = 5.29150
Square Root of 200 - √200 = 14.14214
Square Root of 80 - √80 = 8.94427

Square Root of 674 Solved Examples

Example 1: Solve the equation x² − 674 = 0

Solution:

x² - 674 = 0 i.e. x² = 674
x = ±√674
Since the value of the square root of 674 is 25.962,
⇒ x = +√674 or -√674 = 25.962 or -25.962.
Example 2: If the surface area of a cube is 4044 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 = 4044 in²
⇒ a = ±√674 in
Since length can't be negative,
⇒ a = √674
We know that the square root of 674 is 25.962.
⇒ a = 25.962 in
Example 3: If the surface area of a sphere is 2696π in². Find the radius of the sphere.

Solution:

Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr² = 2696π in²
⇒ r = ±√674 in
Since radius can't be negative,
⇒ r = √674
The square root of 674 is 25.962.
⇒ r = 25.962 in

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FAQs on the Square Root of 674

What is the Value of the Square Root of 674?

The square root of 674 is 25.9615.

Why is the Square Root of 674 an Irrational Number?

Upon prime factorizing 674 i.e. 2¹ × 337¹, 2 is in odd power. Therefore, the square root of 674 is irrational.

Evaluate 12 plus 3 square root 674

The given expression is 12 + 3 √674. We know that the square root of 674 is 25.962. Therefore, 12 + 3 √674 = 12 + 3 × 25.962 = 12 + 77.885 = 89.885

What is the Square of the Square Root of 674?

The square of the square root of 674 is the number 674 itself i.e. (√674)² = (674)^2/2 = 674.

What is the Value of 2 square root 674?

The square root of 674 is 25.962. Therefore, 2 √674 = 2 × 25.962 = 51.923.

What is the Square Root of -674?

The square root of -674 is an imaginary number. It can be written as √-674 = √-1 × √674 = i √674 = 25.961i
where i = √-1 and it is called the imaginary unit.

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