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Square Root of 1282

The square root of 1282 is expressed as √1282 in the radical form and as (1282)^½ or (1282)^0.5 in the exponent form. The square root of 1282 rounded up to 9 decimal places is 35.805027580. It is the positive solution of the equation x² = 1282.

Square Root of 1282: 35.805027579936315
Square Root of 1282 in exponential form: (1282)^½ or (1282)^0.5
Square Root of 1282 in radical form: √1282

Square Root of 1282

1.	What is the Square Root of 1282?
2.	How to find the Square Root of 1282?
3.	Is the Square Root of 1282 Irrational?
4.	FAQs

What is the Square Root of 1282?

The square root of 1282, (or root 1282), is the number which when multiplied by itself gives the product as 1282. Therefore, the square root of 1282 = √1282 = 35.805027579936315.

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How to Find Square Root of 1282?

Square Root of 1282 by Long Division Method

Value of √1282 by Long Division Method

Explanation:

Forming pairs: 12 and 82
Find a number Y (3) such that whose square is <= 12. Now divide 12 by 3 with quotient as 3.
Bring down the next pair 82, to the right of the remainder 3. The new dividend is now 382.
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 5) such that 6Z × Z <= 382. After finding Z, together 6 and Z (5) form a new divisor 65 for the new dividend 382.
Divide 382 by 65 with the quotient as 5, giving the remainder = 382 - 65 × 5 = 382 - 325 = 57.
Now, let's find the decimal places after the quotient 35.
Bring down 00 to the right of this remainder 57. The new dividend is now 5700.
Add the last digit of quotient to divisor i.e. 5 + 65 = 70. To the right of 70, find a digit Z (which is 8) such that 70Z × Z <= 5700. Together they form a new divisor (708) for the new dividend (5700).
Divide 5700 by 708 with the quotient as 8, giving the remainder = 5700 - 708 × 8 = 5700 - 5664 = 36.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 1282.

Therefore, the square root of 1282 by long division method is 35.8 approximately.

Is Square Root of 1282 Irrational?

The actual value of √1282 is undetermined. The value of √1282 up to 25 decimal places is 35.80502757993631262551308. Hence, the square root of 1282 is an irrational number.

☛ Also Check:

Square Root of 23 - √23 = 4.79583
Square Root of 324 - √324 = 18
Square Root of 25 - √25 = 5
Square Root of 400 - √400 = 20
Square Root of 98 - √98 = 9.89949
Square Root of 900 - √900 = 30
Square Root of 27 - √27 = 5.19615

Square Root of 1282 Solved Examples

Example 1: Solve the equation x² − 1282 = 0

Solution:

x² - 1282 = 0 i.e. x² = 1282
x = ±√1282
Since the value of the square root of 1282 is 35.805,
⇒ x = +√1282 or -√1282 = 35.805 or -35.805.
Example 2: If the area of an equilateral triangle is 1282√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 = 1282√3 in²
⇒ a = ±√5128 in
Since length can't be negative,
⇒ a = √5128 = 2 √1282
We know that the square root of 1282 is 35.805.
⇒ a = 71.610 in
Example 3: If the area of a circle is 1282π in². Find the radius of the circle.

Solution:

Let 'r' be the radius of the circle.
⇒ Area of the circle = πr² = 1282π in²
⇒ r = ±√1282 in
Since radius can't be negative,
⇒ r = √1282
The square root of 1282 is 35.805.
⇒ r = 35.805 in

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FAQs on the Square Root of 1282

What is the Value of the Square Root of 1282?

The square root of 1282 is 35.80502.

Why is the Square Root of 1282 an Irrational Number?

Upon prime factorizing 1282 i.e. 2¹ × 641¹, 2 is in odd power. Therefore, the square root of 1282 is irrational.

What is the Square Root of 1282 in Simplest Radical Form?

We need to express 1282 as the product of its prime factors i.e. 1282 = 2 × 641. Therefore, as visible, the radical form of the square root of 1282 cannot be simplified further. Therefore, the simplest radical form of the square root of 1282 can be written as √1282

What is the Value of 11 square root 1282?

The square root of 1282 is 35.805. Therefore, 11 √1282 = 11 × 35.805 = 393.855.

Is the number 1282 a Perfect Square?

The prime factorization of 1282 = 2¹ × 641¹. Here, the prime factor 2 is not in the pair. Therefore, 1282 is not a perfect square.

Evaluate 20 plus 3 square root 1282

The given expression is 20 + 3 √1282. We know that the square root of 1282 is 35.805. Therefore, 20 + 3 √1282 = 20 + 3 × 35.805 = 20 + 107.415 = 127.415

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