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Square Root of 1568

The square root of 1568 is expressed as √1568 in the radical form and as (1568)^½ or (1568)^0.5 in the exponent form. The square root of 1568 rounded up to 9 decimal places is 39.597979746. It is the positive solution of the equation x² = 1568. We can express the square root of 1568 in its lowest radical form as 28 √2.

Square Root of 1568: 39.59797974644666
Square Root of 1568 in exponential form: (1568)^½ or (1568)^0.5
Square Root of 1568 in radical form: √1568 or 28 √2

Square Root of 1568

1.	What is the Square Root of 1568?
2.	How to find the Square Root of 1568?
3.	Is the Square Root of 1568 Irrational?
4.	FAQs

What is the Square Root of 1568?

The square root of 1568, (or root 1568), is the number which when multiplied by itself gives the product as 1568. Therefore, the square root of 1568 = √1568 = 28 √2 = 39.59797974644666.

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How to Find Square Root of 1568?

Square Root of 1568 by Long Division Method

Value of √1568 by Long Division Method

Explanation:

Forming pairs: 15 and 68
Find a number Y (3) such that whose square is <= 15. Now divide 15 by 3 with quotient as 3.
Bring down the next pair 68, to the right of the remainder 6. The new dividend is now 668.
Add the last digit of the quotient (3) to the divisor (3) i.e. 3 + 3 = 6. To the right of 6, find a digit Z (which is 9) such that 6Z × Z <= 668. After finding Z, together 6 and Z (9) form a new divisor 69 for the new dividend 668.
Divide 668 by 69 with the quotient as 9, giving the remainder = 668 - 69 × 9 = 668 - 621 = 47.
Now, let's find the decimal places after the quotient 39.
Bring down 00 to the right of this remainder 47. The new dividend is now 4700.
Add the last digit of quotient to divisor i.e. 9 + 69 = 78. To the right of 78, find a digit Z (which is 5) such that 78Z × Z <= 4700. Together they form a new divisor (785) for the new dividend (4700).
Divide 4700 by 785 with the quotient as 5, giving the remainder = 4700 - 785 × 5 = 4700 - 3925 = 775.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 1568.

Therefore, the square root of 1568 by long division method is 39.5 approximately.

Is Square Root of 1568 Irrational?

The actual value of √1568 is undetermined. The value of √1568 up to 25 decimal places is 39.59797974644666136644728. Hence, the square root of 1568 is an irrational number.

☛ Also Check:

Square Root of 109 - √109 = 10.44031
Square Root of 48 - √48 = 6.92820
Square Root of 37 - √37 = 6.08276
Square Root of 60 - √60 = 7.74597
Square Root of 100 - √100 = 10
Square Root of 40 - √40 = 6.32456
Square Root of 8 - √8 = 2.82843

Square Root of 1568 Solved Examples

Example 1: Solve the equation x² − 1568 = 0

Solution:

x² - 1568 = 0 i.e. x² = 1568
x = ±√1568
Since the value of the square root of 1568 is 39.598,
⇒ x = +√1568 or -√1568 = 39.598 or -39.598.
Example 2: If the surface area of a cube is 9408 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 = 9408 in²
⇒ a = ±√1568 in
Since length can't be negative,
⇒ a = √1568
We know that the square root of 1568 is 39.598.
⇒ a = 39.598 in
Example 3: If the area of a square is 1568 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 = 1568 in²
⇒ a = ±√1568 in
Since length can't be negative,
⇒ a = √1568 = 39.598 in

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FAQs on the Square Root of 1568

What is the Value of the Square Root of 1568?

The square root of 1568 is 39.59797.

Why is the Square Root of 1568 an Irrational Number?

Upon prime factorizing 1568 i.e. 2⁵ × 7², 2 is in odd power. Therefore, the square root of 1568 is irrational.

What is the Value of 11 square root 1568?

The square root of 1568 is 39.598. Therefore, 11 √1568 = 11 × 39.598 = 435.578.

Evaluate 8 plus 9 square root 1568

The given expression is 8 + 9 √1568. We know that the square root of 1568 is 39.598. Therefore, 8 + 9 √1568 = 8 + 9 × 39.598 = 8 + 356.382 = 364.382

What is the Square Root of 1568 in Simplest Radical Form?

We need to express 1568 as the product of its prime factors i.e. 1568 = 2 × 2 × 2 × 2 × 2 × 7 × 7. Therefore, √1568 = √2 × 2 × 2 × 2 × 2 × 7 × 7 = 28 √2. Thus, the square root of 1568 in the lowest radical form is 28 √2.

Is the number 1568 a Perfect Square?

The prime factorization of 1568 = 2⁵ × 7². Here, the prime factor 2 is not in the pair. Therefore, 1568 is not a perfect square.

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