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Square Root of 1008

The square root of 1008 is expressed as √1008 in the radical form and as (1008)^½ or (1008)^0.5 in the exponent form. The square root of 1008 rounded up to 10 decimal places is 31.7490157328. It is the positive solution of the equation x² = 1008. We can express the square root of 1008 in its lowest radical form as 12 √7.

Square Root of 1008: 31.74901573277509
Square Root of 1008 in exponential form: (1008)^½ or (1008)^0.5
Square Root of 1008 in radical form: √1008 or 12 √7

Square Root of 1008

1.	What is the Square Root of 1008?
2.	How to find the Square Root of 1008?
3.	Is the Square Root of 1008 Irrational?
4.	FAQs

What is the Square Root of 1008?

The square root of 1008, (or root 1008), is the number which when multiplied by itself gives the product as 1008. Therefore, the square root of 1008 = √1008 = 12 √7 = 31.74901573277509.

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How to Find Square Root of 1008?

Square Root of 1008 by Long Division Method

Value of √1008 by Long Division Method

Explanation:

Forming pairs: 10 and 08
Find a number Y (3) such that whose square is <= 10. Now divide 10 by 3 with quotient as 3.
Bring down the next pair 08, to the right of the remainder 1. The new dividend is now 108.
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 1) such that 6Z × Z <= 108. After finding Z, together 6 and Z (1) form a new divisor 61 for the new dividend 108.
Divide 108 by 61 with the quotient as 1, giving the remainder = 108 - 61 × 1 = 108 - 61 = 47.
Now, let's find the decimal places after the quotient 31.
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. 1 + 61 = 62. To the right of 62, find a digit Z (which is 7) such that 62Z × Z <= 4700. Together they form a new divisor (627) for the new dividend (4700).
Divide 4700 by 627 with the quotient as 7, giving the remainder = 4700 - 627 × 7 = 4700 - 4389 = 311.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 1008.

Therefore, the square root of 1008 by long division method is 31.7 approx.

Is Square Root of 1008 Irrational?

The actual value of √1008 is undetermined. The value of √1008 up to 25 decimal places is 31.74901573277508708601939. Hence, the square root of 1008 is an irrational number.

☛ Also Check:

Square Root of 1296 - √1296 = 36
Square Root of 29 - √29 = 5.38516
Square Root of 34 - √34 = 5.83095
Square Root of 35 - √35 = 5.91608
Square Root of 1521 - √1521 = 39
Square Root of 162 - √162 = 12.72792
Square Root of 200 - √200 = 14.14214

Square Root of 1008 Solved Examples

Example 1: Solve the equation x² − 1008 = 0

Solution:

x² - 1008 = 0 i.e. x² = 1008
x = ±√1008
Since the value of the square root of 1008 is 31.749,
⇒ x = +√1008 or -√1008 = 31.749 or -31.749.
Example 2: If the area of a square is 1008 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 = 1008 in²
⇒ a = ±√1008 in
Since length can't be negative,
⇒ a = √1008 = 31.749 in
Example 3: If the area of an equilateral triangle is 1008√3 in². Find the length of one of the sides of the triangle.

Solution:

Let 'a' be the length of one of the sides of the equilateral triangle.
⇒ Area of the equilateral triangle = (√3/4)a² = 1008√3 in²
⇒ a = ±√4032 in
Since length can't be negative,
⇒ a = √4032 = 2 √1008
We know that the square root of 1008 is 31.749.
⇒ a = 63.498 in

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FAQs on the Square Root of 1008

What is the Value of the Square Root of 1008?

The square root of 1008 is 31.74901.

Why is the Square Root of 1008 an Irrational Number?

Upon prime factorizing 1008 i.e. 2⁴ × 3² × 7¹, 7 is in odd power. Therefore, the square root of 1008 is irrational.

What is the Value of 20 square root 1008?

The square root of 1008 is 31.749. Therefore, 20 √1008 = 20 × 31.749 = 634.980.

Is the number 1008 a Perfect Square?

The prime factorization of 1008 = 2⁴ × 3² × 7¹. Here, the prime factor 7 is not in the pair. Therefore, 1008 is not a perfect square.

What is the Square of the Square Root of 1008?

The square of the square root of 1008 is the number 1008 itself i.e. (√1008)² = (1008)^2/2 = 1008.

If the Square Root of 1008 is 31.749. Find the Value of the Square Root of 10.08.

Let us represent √10.08 in p/q form i.e. √(1008/100) = 10.08/10 = 3.175. Hence, the value of √10.08 = 3.175

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