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Square Root of 640

The square root of 640 is expressed as √640 in the radical form and as (640)^½ or (640)^0.5 in the exponent form. The square root of 640 rounded up to 10 decimal places is 25.2982212813. It is the positive solution of the equation x² = 640. We can express the square root of 640 in its lowest radical form as 8 √10.

Square Root of 640: 25.298221281347036
Square Root of 640 in exponential form: (640)^½ or (640)^0.5
Square Root of 640 in radical form: √640 or 8 √10

Square Root of 640

1.	What is the Square Root of 640?
2.	How to find the Square Root of 640?
3.	Is the Square Root of 640 Irrational?
4.	FAQs

What is the Square Root of 640?

The square root of 640, (or root 640), is the number which when multiplied by itself gives the product as 640. Therefore, the square root of 640 = √640 = 8 √10 = 25.298221281347036.

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How to Find Square Root of 640?

Square Root of 640 by Long Division Method

Value of √640 by Long Division Method

Explanation:

Forming pairs: 06 and 40
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 40, to the right of the remainder 2. The new dividend is now 240.
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 <= 240. After finding Z, together 4 and Z (5) form a new divisor 45 for the new dividend 240.
Divide 240 by 45 with the quotient as 5, giving the remainder = 240 - 45 × 5 = 240 - 225 = 15.
Now, let's find the decimal places after the quotient 25.
Bring down 00 to the right of this remainder 15. The new dividend is now 1500.
Add the last digit of quotient to divisor i.e. 5 + 45 = 50. To the right of 50, find a digit Z (which is 2) such that 50Z × Z <= 1500. Together they form a new divisor (502) for the new dividend (1500).
Divide 1500 by 502 with the quotient as 2, giving the remainder = 1500 - 502 × 2 = 1500 - 1004 = 496.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 640.

Therefore, the square root of 640 by long division method is 25.2 approximately.

Is Square Root of 640 Irrational?

The actual value of √640 is undetermined. The value of √640 up to 25 decimal places is 25.29822128134703465599115. Hence, the square root of 640 is an irrational number.

☛ Also Check:

Square Root of 512 - √512 = 22.62742
Square Root of 149 - √149 = 12.20656
Square Root of 841 - √841 = 29
Square Root of 169 - √169 = 13
Square Root of 16 - √16 = 4
Square Root of 45 - √45 = 6.70820
Square Root of 15 - √15 = 3.87298

Square Root of 640 Solved Examples

Example 1: Solve the equation x² − 640 = 0

Solution:

x² - 640 = 0 i.e. x² = 640
x = ±√640
Since the value of the square root of 640 is 25.298,
⇒ x = +√640 or -√640 = 25.298 or -25.298.
Example 2: If the surface area of a cube is 3840 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 = 3840 in²
⇒ a = ±√640 in
Since length can't be negative,
⇒ a = √640
We know that the square root of 640 is 25.298.
⇒ a = 25.298 in
Example 3: If the area of a square is 640 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 = 640 in²
⇒ a = ±√640 in
Since length can't be negative,
⇒ a = √640 = 25.298 in

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FAQs on the Square Root of 640

What is the Value of the Square Root of 640?

The square root of 640 is 25.29822.

Why is the Square Root of 640 an Irrational Number?

Upon prime factorizing 640 i.e. 2⁷ × 5¹, 2 is in odd power. Therefore, the square root of 640 is irrational.

What is the Square of the Square Root of 640?

The square of the square root of 640 is the number 640 itself i.e. (√640)² = (640)^2/2 = 640.

What is the Value of 6 square root 640?

The square root of 640 is 25.298. Therefore, 6 √640 = 6 × 25.298 = 151.789.

If the Square Root of 640 is 25.298. Find the Value of the Square Root of 6.4.

Let us represent √6.4 in p/q form i.e. √(640/100) = 6.4/10 = 2.530. Hence, the value of √6.4 = 2.530

What is the Square Root of 640 in Simplest Radical Form?

We need to express 640 as the product of its prime factors i.e. 640 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 5. Therefore, √640 = √2 × 2 × 2 × 2 × 2 × 2 × 2 × 5 = 8 √10. Thus, the square root of 640 in the lowest radical form is 8 √10.

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