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Square Root of 4096

The square root of 4096 is expressed as √4096 in the radical form and as (4096)^½ or (4096)^0.5 in the exponent form. The square root of 4096 is 64. It is the positive solution of the equation x² = 4096. The number 4096 is a perfect square.

Square Root of 4096: 64
Square Root of 4096 in exponential form: (4096)^½ or (4096)^0.5
Square Root of 4096 in radical form: √4096

Square Root of 4096

1.	What is the Square Root of 4096?
2.	How to find the Square Root of 4096?
3.	Is the Square Root of 4096 Rational?
4.	FAQs

What is the Square Root of 4096?

The square root of 4096, (or root 4096), is the number which when multiplied by itself gives the product as 4096. Therefore, the square root of 4096 = √4096 = 64.

☛ Check: Square Root Calculator

How to Find Square Root of 4096?

Square Root of 4096 by Long Division Method

Value of √4096 by Long Division Method

Explanation:

Forming pairs: 40 and 96
Find a number Y (6) such that whose square is <= 40. Now divide 40 by 6 with quotient as 6.
Bring down the next pair 96, to the right of the remainder 4. The new dividend is now 496.
Add the last digit of the quotient (6) to the divisor (6) i.e. 6 + 6 = 12. To the right of 12, find a digit Z (which is 4) such that 12Z × Z <= 496. After finding Z, together 12 and Z (4) form a new divisor 124 for the new dividend 496.
Divide 496 by 124 with the quotient as 4, giving the remainder = 496 - 124 × 4 = 496 - 496 = 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 4096 by long division method is 64.

Is Square Root of 4096 Rational?

The value of √4096 is 64. Hence, the square root of 4096 is a rational number.

☛ Also Check:

Square Root of 109 - √109 = 10.44031
Square Root of 1024 - √1024 = 32
Square Root of 100 - √100 = 10
Square Root of 13 - √13 = 3.60555
Square Root of 1000 - √1000 = 31.62278
Square Root of 169 - √169 = 13
Square Root of 22 - √22 = 4.69042

Square Root of 4096 Solved Examples

Example 1: Solve the equation x² − 4096 = 0

Solution:

x² - 4096 = 0 i.e. x² = 4096
x = ±√4096
Since the value of the square root of 4096 is 64,
⇒ x = +√4096 or -√4096 = 64 or -64.
Example 2: If the area of a square is 4096 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 = 4096 in²
⇒ a = ±√4096 in
Since length can't be negative,
⇒ a = √4096 = 64 in
Example 3: If the surface area of a sphere is 16384π in². Find the radius of the sphere.

Solution:

Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr² = 16384π in²
⇒ r = ±√4096 in
Since radius can't be negative,
⇒ r = √4096
The square root of 4096 is 64.
⇒ r = 64 in

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FAQs on the Square Root of 4096

What is the Value of the Square Root of 4096?

The square root of 4096 is 64.

Why is the Square Root of 4096 a Rational Number?

Upon prime factorizing 4096 i.e. 2¹², we find that all the prime factors are in even power. This implies that the square root of 4096 is a positive integer. Therefore, the square root of 4096 is rational.

Evaluate 2 plus 9 square root 4096

The given expression is 2 + 9 √4096. We know that the square root of 4096 is 64. Therefore, 2 + 9 √4096 = 2 + 9 × 64 = 2 + 576 = 578

What is the Square of the Square Root of 4096?

The square of the square root of 4096 is the number 4096 itself i.e. (√4096)² = (4096)^2/2 = 4096.

What is the Value of 2 square root 4096?

The square root of 4096 is 64. Therefore, 2 √4096 = 2 × 64 = 128.

If the Square Root of 4096 is 64. Find the Value of the Square Root of 40.96.

Let us represent √40.96 in p/q form i.e. √(4096/100) = 40.96/10 = 6. Hence, the value of √40.96 = 6

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