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Square Root of 1300

The square root of 1300 is expressed as √1300 in the radical form and as (1300)^½ or (1300)^0.5 in the exponent form. The square root of 1300 rounded up to 8 decimal places is 36.05551275. It is the positive solution of the equation x² = 1300. We can express the square root of 1300 in its lowest radical form as 10 √13.

Square Root of 1300: 36.05551275463989
Square Root of 1300 in exponential form: (1300)^½ or (1300)^0.5
Square Root of 1300 in radical form: √1300 or 10 √13

Square Root of 1300

1.	What is the Square Root of 1300?
2.	How to find the Square Root of 1300?
3.	Is the Square Root of 1300 Irrational?
4.	FAQs

What is the Square Root of 1300?

The square root of 1300, (or root 1300), is the number which when multiplied by itself gives the product as 1300. Therefore, the square root of 1300 = √1300 = 10 √13 = 36.05551275463989.

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How to Find Square Root of 1300?

Square Root of 1300 by Long Division Method

Value of √1300 by Long Division Method

Explanation:

Forming pairs: 13 and 00
Find a number Y (3) such that whose square is <= 13. Now divide 13 by 3 with quotient as 3.
Bring down the next pair 00, to the right of the remainder 4. The new dividend is now 400.
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 6) such that 6Z × Z <= 400. After finding Z, together 6 and Z (6) form a new divisor 66 for the new dividend 400.
Divide 400 by 66 with the quotient as 6, giving the remainder = 400 - 66 × 6 = 400 - 396 = 4.
Now, let's find the decimal places after the quotient 36.
Bring down 00 to the right of this remainder 4. The new dividend is now 400.
Add the last digit of quotient to divisor i.e. 6 + 66 = 72. To the right of 72, find a digit Z (which is 0) such that 72Z × Z <= 400. Together they form a new divisor (720) for the new dividend (400).
Divide 400 by 720 with the quotient as 0, giving the remainder = 400 - 720 × 0 = 400 - 0 = 400.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 1300.

Therefore, the square root of 1300 by long division method is 36.0 approximately.

Is Square Root of 1300 Irrational?

The actual value of √1300 is undetermined. The value of √1300 up to 25 decimal places is 36.05551275463989293119221. Hence, the square root of 1300 is an irrational number.

☛ Also Check:

Square Root of 90 - √90 = 9.48683
Square Root of 240 - √240 = 15.49193
Square Root of 1681 - √1681 = 41
Square Root of 361 - √361 = 19
Square Root of 192 - √192 = 13.85641
Square Root of 1024 - √1024 = 32
Square Root of 11 - √11 = 3.31662

Square Root of 1300 Solved Examples

Example 1: Solve the equation x² − 1300 = 0

Solution:

x² - 1300 = 0 i.e. x² = 1300
x = ±√1300
Since the value of the square root of 1300 is 36.056,
⇒ x = +√1300 or -√1300 = 36.056 or -36.056.
Example 2: If the area of an equilateral triangle is 1300√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 = 1300√3 in²
⇒ a = ±√5200 in
Since length can't be negative,
⇒ a = √5200 = 2 √1300
We know that the square root of 1300 is 36.056.
⇒ a = 72.111 in
Example 3: If the area of a circle is 1300π in². Find the radius of the circle.

Solution:

Let 'r' be the radius of the circle.
⇒ Area of the circle = πr² = 1300π in²
⇒ r = ±√1300 in
Since radius can't be negative,
⇒ r = √1300
The square root of 1300 is 36.056.
⇒ r = 36.056 in

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FAQs on the Square Root of 1300

What is the Value of the Square Root of 1300?

The square root of 1300 is 36.05551.

Why is the Square Root of 1300 an Irrational Number?

Upon prime factorizing 1300 i.e. 2² × 5² × 13¹, 13 is in odd power. Therefore, the square root of 1300 is irrational.

What is the Square Root of 1300 in Simplest Radical Form?

We need to express 1300 as the product of its prime factors i.e. 1300 = 2 × 2 × 5 × 5 × 13. Therefore, √1300 = √2 × 2 × 5 × 5 × 13 = 10 √13. Thus, the square root of 1300 in the lowest radical form is 10 √13.

What is the Square of the Square Root of 1300?

The square of the square root of 1300 is the number 1300 itself i.e. (√1300)² = (1300)^2/2 = 1300.

What is the Square Root of -1300?

The square root of -1300 is an imaginary number. It can be written as √-1300 = √-1 × √1300 = i √1300 = 36.055i
where i = √-1 and it is called the imaginary unit.

What is the Value of 15 square root 1300?

The square root of 1300 is 36.056. Therefore, 15 √1300 = 15 × 36.056 = 540.833.

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