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Square Root of 1849

The square root of 1849 is expressed as √1849 in the radical form and as (1849)^½ or (1849)^0.5 in the exponent form. The square root of 1849 is 43. It is the positive solution of the equation x² = 1849. The number 1849 is a perfect square.

Square Root of 1849: 43
Square Root of 1849 in exponential form: (1849)^½ or (1849)^0.5
Square Root of 1849 in radical form: √1849

Square Root of 1849

1.	What is the Square Root of 1849?
2.	How to find the Square Root of 1849?
3.	Is the Square Root of 1849 Rational?
4.	FAQs

What is the Square Root of 1849?

The square root of 1849, (or root 1849), is the number which when multiplied by itself gives the product as 1849. Therefore, the square root of 1849 = √1849 = 43.

☛ Check: Square Root Calculator

How to Find Square Root of 1849?

Square Root of 1849 by Long Division Method

Value of √1849 by Long Division Method

Explanation:

Forming pairs: 18 and 49
Find a number Y (4) such that whose square is <= 18. Now divide 18 by 4 with quotient as 4.
Bring down the next pair 49, to the right of the remainder 2. The new dividend is now 249.
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 3) such that 8Z × Z <= 249. After finding Z, together 8 and Z (3) form a new divisor 83 for the new dividend 249.
Divide 249 by 83 with the quotient as 3, giving the remainder = 249 - 83 × 3 = 249 - 249 = 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 1849 by long division method is 43.

Is Square Root of 1849 Rational?

The value of √1849 is 43. Hence, the square root of 1849 is a rational number.

☛ Also Check:

Square Root of 1296 - √1296 = 36
Square Root of 325 - √325 = 18.02776
Square Root of 1521 - √1521 = 39
Square Root of 125 - √125 = 11.18034
Square Root of 13 - √13 = 3.60555
Square Root of 68 - √68 = 8.24621
Square Root of 75 - √75 = 8.66025

Square Root of 1849 Solved Examples

Example 1: Solve the equation x² − 1849 = 0

Solution:

x² - 1849 = 0 i.e. x² = 1849
x = ±√1849
Since the value of the square root of 1849 is 43,
⇒ x = +√1849 or -√1849 = 43 or -43.
Example 2: If the area of an equilateral triangle is 1849√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 = 1849√3 in²
⇒ a = ±√7396 in
Since length can't be negative,
⇒ a = √7396 = 2 √1849
We know that the square root of 1849 is 43.
⇒ a = 86 in
Example 3: If the area of a square is 1849 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 = 1849 in²
⇒ a = ±√1849 in
Since length can't be negative,
⇒ a = √1849 = 43 in

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FAQs on the Square Root of 1849

What is the Value of the Square Root of 1849?

The square root of 1849 is 43.

Why is the Square Root of 1849 a Rational Number?

Upon prime factorizing 1849 i.e. 43², we find that all the prime factors are in even power. This implies that the square root of 1849 is a positive integer. Therefore, the square root of 1849 is rational.

Evaluate 4 plus 2 square root 1849

The given expression is 4 + 2 √1849. We know that the square root of 1849 is 43. Therefore, 4 + 2 √1849 = 4 + 2 × 43 = 4 + 86 = 90

What is the Square Root of -1849?

The square root of -1849 is an imaginary number. It can be written as √-1849 = √-1 × √1849 = i √1849 = 43i
where i = √-1 and it is called the imaginary unit.

What is the Square of the Square Root of 1849?

The square of the square root of 1849 is the number 1849 itself i.e. (√1849)² = (1849)^2/2 = 1849.

What is the Value of 20 square root 1849?

The square root of 1849 is 43. Therefore, 20 √1849 = 20 × 43 = 860.

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