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Square Root of 1729

The square root of 1729 is expressed as √1729 in the radical form and as (1729)^½ or (1729)^0.5 in the exponent form. The square root of 1729 rounded up to 7 decimal places is 41.5812458. It is the positive solution of the equation x² = 1729.

Square Root of 1729: 41.58124577258358
Square Root of 1729 in exponential form: (1729)^½ or (1729)^0.5
Square Root of 1729 in radical form: √1729

Square Root of 1729

1.	What is the Square Root of 1729?
2.	How to find the Square Root of 1729?
3.	Is the Square Root of 1729 Irrational?
4.	FAQs

What is the Square Root of 1729?

The square root of 1729, (or root 1729), is the number which when multiplied by itself gives the product as 1729. Therefore, the square root of 1729 = √1729 = 41.58124577258358.

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How to Find Square Root of 1729?

Square Root of 1729 by Long Division Method

Value of √1729 by Long Division Method

Explanation:

Forming pairs: 17 and 29
Find a number Y (4) such that whose square is <= 17. Now divide 17 by 4 with quotient as 4.
Bring down the next pair 29, to the right of the remainder 1. The new dividend is now 129.
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 1) such that 8Z × Z <= 129. After finding Z, together 8 and Z (1) form a new divisor 81 for the new dividend 129.
Divide 129 by 81 with the quotient as 1, giving the remainder = 129 - 81 × 1 = 129 - 81 = 48.
Now, let's find the decimal places after the quotient 41.
Bring down 00 to the right of this remainder 48. The new dividend is now 4800.
Add the last digit of quotient to divisor i.e. 1 + 81 = 82. To the right of 82, find a digit Z (which is 5) such that 82Z × Z <= 4800. Together they form a new divisor (825) for the new dividend (4800).
Divide 4800 by 825 with the quotient as 5, giving the remainder = 4800 - 825 × 5 = 4800 - 4125 = 675.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 1729.

Therefore, the square root of 1729 by long division method is 41.5 approx.

Is Square Root of 1729 Irrational?

The actual value of √1729 is undetermined. The value of √1729 up to 25 decimal places is 41.58124577258358189028021. Hence, the square root of 1729 is an irrational number.

☛ Also Check:

Square Root of 12 - √12 = 3.46410
Square Root of 361 - √361 = 19
Square Root of 196 - √196 = 14
Square Root of 900 - √900 = 30
Square Root of 72 - √72 = 8.48528
Square Root of 60 - √60 = 7.74597
Square Root of 17 - √17 = 4.12311

Square Root of 1729 Solved Examples

Example 1: Solve the equation x² − 1729 = 0

Solution:

x² - 1729 = 0 i.e. x² = 1729
x = ±√1729
Since the value of the square root of 1729 is 41.581,
⇒ x = +√1729 or -√1729 = 41.581 or -41.581.
Example 2: If the area of a circle is 1729π in². Find the radius of the circle.

Solution:

Let 'r' be the radius of the circle.
⇒ Area of the circle = πr² = 1729π in²
⇒ r = ±√1729 in
Since radius can't be negative,
⇒ r = √1729
The square root of 1729 is 41.581.
⇒ r = 41.581 in
Example 3: If the area of a square is 1729 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 = 1729 in²
⇒ a = ±√1729 in
Since length can't be negative,
⇒ a = √1729 = 41.581 in

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FAQs on the Square Root of 1729

What is the Value of the Square Root of 1729?

The square root of 1729 is 41.58124.

Why is the Square Root of 1729 an Irrational Number?

Upon prime factorizing 1729 i.e. 7¹ × 13¹ × 19¹, 7 is in odd power. Therefore, the square root of 1729 is irrational.

Is the number 1729 a Perfect Square?

The prime factorization of 1729 = 7¹ × 13¹ × 19¹. Here, the prime factor 7 is not in the pair. Therefore, 1729 is not a perfect square.

What is the Square Root of -1729?

The square root of -1729 is an imaginary number. It can be written as √-1729 = √-1 × √1729 = i √1729 = 41.581i
where i = √-1 and it is called the imaginary unit.

What is the Square Root of 1729 in Simplest Radical Form?

We need to express 1729 as the product of its prime factors i.e. 1729 = 7 × 13 × 19. Therefore, as visible, the radical form of the square root of 1729 cannot be simplified further. Therefore, the simplest radical form of the square root of 1729 can be written as √1729

If the Square Root of 1729 is 41.581. Find the Value of the Square Root of 17.29.

Let us represent √17.29 in p/q form i.e. √(1729/100) = 17.29/10 = 4.158. Hence, the value of √17.29 = 4.158

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