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Square Root of 5200

The square root of 5200 is expressed as √5200 in the radical form and as (5200)^½ or (5200)^0.5 in the exponent form. The square root of 5200 rounded up to 10 decimal places is 72.1110255093. It is the positive solution of the equation x² = 5200. We can express the square root of 5200 in its lowest radical form as 20 √13.

Square Root of 5200: 72.11102550927978
Square Root of 5200 in exponential form: (5200)^½ or (5200)^0.5
Square Root of 5200 in radical form: √5200 or 20 √13

Square Root of 5200

1.	What is the Square Root of 5200?
2.	How to find the Square Root of 5200?
3.	Is the Square Root of 5200 Irrational?
4.	FAQs

What is the Square Root of 5200?

The square root of 5200, (or root 5200), is the number which when multiplied by itself gives the product as 5200. Therefore, the square root of 5200 = √5200 = 20 √13 = 72.11102550927978.

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How to Find Square Root of 5200?

Square Root of 5200 by Long Division Method

Value of √5200 by Long Division Method

Explanation:

Forming pairs: 52 and 00
Find a number Y (7) such that whose square is <= 52. Now divide 52 by 7 with quotient as 7.
Bring down the next pair 00, to the right of the remainder 3. The new dividend is now 300.
Add the last digit of the quotient (7) to the divisor (7) i.e. 7 + 7 = 14. To the right of 14, find a digit Z (which is 2) such that 14Z × Z <= 300. After finding Z, together 14 and Z (2) form a new divisor 142 for the new dividend 300.
Divide 300 by 142 with the quotient as 2, giving the remainder = 300 - 142 × 2 = 300 - 284 = 16.
Now, let's find the decimal places after the quotient 72.
Bring down 00 to the right of this remainder 16. The new dividend is now 1600.
Add the last digit of quotient to divisor i.e. 2 + 142 = 144. To the right of 144, find a digit Z (which is 1) such that 144Z × Z <= 1600. Together they form a new divisor (1441) for the new dividend (1600).
Divide 1600 by 1441 with the quotient as 1, giving the remainder = 1600 - 1441 × 1 = 1600 - 1441 = 159.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 5200.

Therefore, the square root of 5200 by long division method is 72.1 approximately.

Is Square Root of 5200 Irrational?

The actual value of √5200 is undetermined. The value of √5200 up to 25 decimal places is 72.11102550927978586238443. Hence, the square root of 5200 is an irrational number.

☛ Also Check:

Square Root of 108 - √108 = 10.39230
Square Root of 12 - √12 = 3.46410
Square Root of 1681 - √1681 = 41
Square Root of 105 - √105 = 10.24695
Square Root of 63 - √63 = 7.93725
Square Root of 27 - √27 = 5.19615
Square Root of 73 - √73 = 8.54400

Square Root of 5200 Solved Examples

Example 1: Solve the equation x² − 5200 = 0

Solution:

x² - 5200 = 0 i.e. x² = 5200
x = ±√5200
Since the value of the square root of 5200 is 72.111,
⇒ x = +√5200 or -√5200 = 72.111 or -72.111.
Example 2: If the area of an equilateral triangle is 5200√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 = 5200√3 in²
⇒ a = ±√20800 in
Since length can't be negative,
⇒ a = √20800 = 2 √5200
We know that the square root of 5200 is 72.111.
⇒ a = 144.222 in
Example 3: If the surface area of a cube is 31200 in². Find the length of the side of the cube.

Solution:

Let 'a' be the length of the side of the cube.
⇒ Area of the cube = 6a² = 31200 in²
⇒ a = ±√5200 in
Since length can't be negative,
⇒ a = √5200
We know that the square root of 5200 is 72.111.
⇒ a = 72.111 in

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FAQs on the Square Root of 5200

What is the Value of the Square Root of 5200?

The square root of 5200 is 72.11102.

Why is the Square Root of 5200 an Irrational Number?

Upon prime factorizing 5200 i.e. 2⁴ × 5² × 13¹, 13 is in odd power. Therefore, the square root of 5200 is irrational.

Is the number 5200 a Perfect Square?

The prime factorization of 5200 = 2⁴ × 5² × 13¹. Here, the prime factor 13 is not in the pair. Therefore, 5200 is not a perfect square.

What is the Square Root of 5200 in Simplest Radical Form?

We need to express 5200 as the product of its prime factors i.e. 5200 = 2 × 2 × 2 × 2 × 5 × 5 × 13. Therefore, √5200 = √2 × 2 × 2 × 2 × 5 × 5 × 13 = 20 √13. Thus, the square root of 5200 in the lowest radical form is 20 √13.

Evaluate 12 plus 3 square root 5200

The given expression is 12 + 3 √5200. We know that the square root of 5200 is 72.111. Therefore, 12 + 3 √5200 = 12 + 3 × 72.111 = 12 + 216.333 = 228.333

What is the Value of 6 square root 5200?

The square root of 5200 is 72.111. Therefore, 6 √5200 = 6 × 72.111 = 432.666.

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