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Square Root of 2048

The square root of 2048 is expressed as √2048 in the radical form and as (2048)^½ or (2048)^0.5 in the exponent form. The square root of 2048 rounded up to 6 decimal places is 45.254834. It is the positive solution of the equation x² = 2048. We can express the square root of 2048 in its lowest radical form as 32 √2.

Square Root of 2048: 45.254833995939045
Square Root of 2048 in exponential form: (2048)^½ or (2048)^0.5
Square Root of 2048 in radical form: √2048 or 32 √2

Square Root of 2048

1.	What is the Square Root of 2048?
2.	How to find the Square Root of 2048?
3.	Is the Square Root of 2048 Irrational?
4.	FAQs

What is the Square Root of 2048?

The square root of 2048, (or root 2048), is the number which when multiplied by itself gives the product as 2048. Therefore, the square root of 2048 = √2048 = 32 √2 = 45.254833995939045.

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How to Find Square Root of 2048?

Square Root of 2048 by Long Division Method

Value of √2048 by Long Division Method

Explanation:

Forming pairs: 20 and 48
Find a number Y (4) such that whose square is <= 20. Now divide 20 by 4 with quotient as 4.
Bring down the next pair 48, to the right of the remainder 4. The new dividend is now 448.
Add the last digit of the quotient (4) to the divisor (4) i.e. 4 + 4 = 8. To the right of 8, find a digit Z (which is 5) such that 8Z × Z <= 448. After finding Z, together 8 and Z (5) form a new divisor 85 for the new dividend 448.
Divide 448 by 85 with the quotient as 5, giving the remainder = 448 - 85 × 5 = 448 - 425 = 23.
Now, let's find the decimal places after the quotient 45.
Bring down 00 to the right of this remainder 23. The new dividend is now 2300.
Add the last digit of quotient to divisor i.e. 5 + 85 = 90. To the right of 90, find a digit Z (which is 2) such that 90Z × Z <= 2300. Together they form a new divisor (902) for the new dividend (2300).
Divide 2300 by 902 with the quotient as 2, giving the remainder = 2300 - 902 × 2 = 2300 - 1804 = 496.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 2048.

Therefore, the square root of 2048 by long division method is 45.2 approx.

Is Square Root of 2048 Irrational?

The actual value of √2048 is undetermined. The value of √2048 up to 25 decimal places is 45.25483399593904156165404. Hence, the square root of 2048 is an irrational number.

☛ Also Check:

Square Root of 74 - √74 = 8.60233
Square Root of 109 - √109 = 10.44031
Square Root of 72 - √72 = 8.48528
Square Root of 1296 - √1296 = 36
Square Root of 162 - √162 = 12.72792
Square Root of 125 - √125 = 11.18034
Square Root of 192 - √192 = 13.85641

Square Root of 2048 Solved Examples

Example 1: Solve the equation x² − 2048 = 0

Solution:

x² - 2048 = 0 i.e. x² = 2048
x = ±√2048
Since the value of the square root of 2048 is 45.255,
⇒ x = +√2048 or -√2048 = 45.255 or -45.255.
Example 2: If the area of a circle is 2048π in². Find the radius of the circle.

Solution:

Let 'r' be the radius of the circle.
⇒ Area of the circle = πr² = 2048π in²
⇒ r = ±√2048 in
Since radius can't be negative,
⇒ r = √2048
The square root of 2048 is 45.255.
⇒ r = 45.255 in
Example 3: If the surface area of a sphere is 8192π in². Find the radius of the sphere.

Solution:

Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr² = 8192π in²
⇒ r = ±√2048 in
Since radius can't be negative,
⇒ r = √2048
The square root of 2048 is 45.255.
⇒ r = 45.255 in

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FAQs on the Square Root of 2048

What is the Value of the Square Root of 2048?

The square root of 2048 is 45.25483.

Why is the Square Root of 2048 an Irrational Number?

Upon prime factorizing 2048 i.e. 2¹¹, 2 is in odd power. Therefore, the square root of 2048 is irrational.

What is the Square Root of -2048?

The square root of -2048 is an imaginary number. It can be written as √-2048 = √-1 × √2048 = i √2048 = 45.254i
where i = √-1 and it is called the imaginary unit.

Evaluate 18 plus 2 square root 2048

The given expression is 18 + 2 √2048. We know that the square root of 2048 is 45.255. Therefore, 18 + 2 √2048 = 18 + 2 × 45.255 = 18 + 90.510 = 108.510

What is the Square Root of 2048 in Simplest Radical Form?

We need to express 2048 as the product of its prime factors i.e. 2048 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2. Therefore, √2048 = √2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 32 √2. Thus, the square root of 2048 in the lowest radical form is 32 √2.

What is the Value of 3 square root 2048?

The square root of 2048 is 45.255. Therefore, 3 √2048 = 3 × 45.255 = 135.765.

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