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Square Root of 6400

The square root of 6400 is expressed as √6400 in the radical form and as (6400)^½ or (6400)^0.5 in the exponent form. The square root of 6400 is 80. It is the positive solution of the equation x² = 6400. The number 6400 is a perfect square.

Square Root of 6400: 80
Square Root of 6400 in exponential form: (6400)^½ or (6400)^0.5
Square Root of 6400 in radical form: √6400

Square Root of 6400

1.	What is the Square Root of 6400?
2.	How to find the Square Root of 6400?
3.	Is the Square Root of 6400 Rational?
4.	FAQs

What is the Square Root of 6400?

The square root of 6400, (or root 6400), is the number which when multiplied by itself gives the product as 6400. Therefore, the square root of 6400 = √6400 = 80.

☛ Check: Square Root Calculator

How to Find Square Root of 6400?

Square Root of 6400 by Long Division Method

Value of √6400 by Long Division Method

Explanation:

Forming pairs: 64 and 00
Find a number Y (8) such that whose square is <= 64. Now divide 64 by 8 with quotient as 8.
Bring down the next pair 00, to the right of the remainder 0. The new dividend is now 0.
Add the last digit of the quotient (8) to the divisor (8) i.e. 8 + 8 = 16. To the right of 16, find a digit Z (which is 0) such that 16Z × Z <= 0. After finding Z, together 16 and Z (0) form a new divisor 160 for the new dividend 0.
Divide 0 by 160 with the quotient as 0, giving the remainder = 0 - 160 × 0 = 0 - 0 = 0.
We stop the process since the remainder is now 0 and there are no more digits that can be brought down.

Therefore, the square root of 6400 by long division method is 80.

Is Square Root of 6400 Rational?

The value of √6400 is 80. Hence, the square root of 6400 is a rational number.

☛ Also Check:

Square Root of 136 - √136 = 11.66190
Square Root of 256 - √256 = 16
Square Root of 320 - √320 = 17.88854
Square Root of 75 - √75 = 8.66025
Square Root of 29 - √29 = 5.38516
Square Root of 33 - √33 = 5.74456
Square Root of 51 - √51 = 7.14143

Square Root of 6400 Solved Examples

Example 1: Solve the equation x² − 6400 = 0

Solution:

x² - 6400 = 0 i.e. x² = 6400
x = ±√6400
Since the value of the square root of 6400 is 80,
⇒ x = +√6400 or -√6400 = 80 or -80.
Example 2: If the area of a circle is 6400π in². Find the radius of the circle.

Solution:

Let 'r' be the radius of the circle.
⇒ Area of the circle = πr² = 6400π in²
⇒ r = ±√6400 in
Since radius can't be negative,
⇒ r = √6400
Square root of 6400 is 80.
⇒ r = 80 in
Example 3: If the surface area of a sphere is 25600π in². Find the radius of the sphere.

Solution:

Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr² = 25600π in²
⇒ r = ±√6400 in
Since radius can't be negative,
⇒ r = √6400
The square root of 6400 is 80.
⇒ r = 80 in

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FAQs on the Square Root of 6400

What is the Value of the Square Root of 6400?

The square root of 6400 is 80.

Why is the Square Root of 6400 a Rational Number?

Upon prime factorizing 6400 i.e. 2⁸ × 5², we find that all the prime factors are in even power. This implies that the square root of 6400 is a positive integer. Therefore, the square root of 6400 is rational.

Is the number 6400 a Perfect Square?

The prime factorization of 6400 = 2⁸ × 5². Here, all the numbers are in the power of 2. This implies that the square root of 6400 is a positive integer. Therefore, 6400 is a perfect square.

What is the Square Root of -6400?

The square root of -6400 is an imaginary number. It can be written as √-6400 = √-1 × √6400 = i √6400 = 80i
where i = √-1 and it is called the imaginary unit.

What is the Value of 18 square root 6400?

The square root of 6400 is 80. Therefore, 18 √6400 = 18 × 80 = 1440.

What is the Square of the Square Root of 6400?

The square of the square root of 6400 is the number 6400 itself i.e. (√6400)² = (6400)^2/2 = 6400.

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