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Square Root of 7500

The square root of 7500 is expressed as √7500 in the radical form and as (7500)^½ or (7500)^0.5 in the exponent form. The square root of 7500 rounded up to 5 decimal places is 86.60254. It is the positive solution of the equation x² = 7500. We can express the square root of 7500 in its lowest radical form as 50 √3.

Square Root of 7500: 86.60254037844386
Square Root of 7500 in exponential form: (7500)^½ or (7500)^0.5
Square Root of 7500 in radical form: √7500 or 50 √3

Square Root of 7500

1.	What is the Square Root of 7500?
2.	How to find the Square Root of 7500?
3.	Is the Square Root of 7500 Irrational?
4.	FAQs

What is the Square Root of 7500?

The square root of 7500, (or root 7500), is the number which when multiplied by itself gives the product as 7500. Therefore, the square root of 7500 = √7500 = 50 √3 = 86.60254037844386.

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How to Find Square Root of 7500?

Square Root of 7500 by Long Division Method

Value of √7500 by Long Division Method

Explanation:

Forming pairs: 75 and 00
Find a number Y (8) such that whose square is <= 75. Now divide 75 by 8 with quotient as 8.
Bring down the next pair 00, to the right of the remainder 11. The new dividend is now 1100.
Add the last digit of the quotient (8) to the divisor (8) i.e. 8 + 8 = 16. To the right of 16, find a digit Z (which is 6) such that 16Z × Z <= 1100. After finding Z, together 16 and Z (6) form a new divisor 166 for the new dividend 1100.
Divide 1100 by 166 with the quotient as 6, giving the remainder = 1100 - 166 × 6 = 1100 - 996 = 104.
Now, let's find the decimal places after the quotient 86.
Bring down 00 to the right of this remainder 104. The new dividend is now 10400.
Add the last digit of quotient to divisor i.e. 6 + 166 = 172. To the right of 172, find a digit Z (which is 6) such that 172Z × Z <= 10400. Together they form a new divisor (1726) for the new dividend (10400).
Divide 10400 by 1726 with the quotient as 6, giving the remainder = 10400 - 1726 × 6 = 10400 - 10356 = 44.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 7500.

Therefore, the square root of 7500 by long division method is 86.6 approximately.

Is Square Root of 7500 Irrational?

The actual value of √7500 is undetermined. The value of √7500 up to 25 decimal places is 86.60254037844386467637232. Hence, the square root of 7500 is an irrational number.

☛ Also Check:

Square Root of 96 - √96 = 9.79796
Square Root of 12 - √12 = 3.46410
Square Root of 325 - √325 = 18.02776
Square Root of 324 - √324 = 18
Square Root of 90 - √90 = 9.48683
Square Root of 45 - √45 = 6.70820
Square Root of 26 - √26 = 5.09902

Square Root of 7500 Solved Examples

Example 1: Solve the equation x² − 7500 = 0

Solution:

x² - 7500 = 0 i.e. x² = 7500
x = ±√7500
Since the value of the square root of 7500 is 86.603,
⇒ x = +√7500 or -√7500 = 86.603 or -86.603.
Example 2: If the surface area of a cube is 45000 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 = 45000 in²
⇒ a = ±√7500 in
Since length can't be negative,
⇒ a = √7500
We know that the square root of 7500 is 86.603.
⇒ a = 86.603 in
Example 3: If the area of a circle is 7500π in². Find the radius of the circle.

Solution:

Let 'r' be the radius of the circle.
⇒ Area of the circle = πr² = 7500π in²
⇒ r = ±√7500 in
Since radius can't be negative,
⇒ r = √7500
The square root of 7500 is 86.603.
⇒ r = 86.603 in

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FAQs on the Square Root of 7500

What is the Value of the Square Root of 7500?

The square root of 7500 is 86.60254.

Why is the Square Root of 7500 an Irrational Number?

Upon prime factorizing 7500 i.e. 2² × 3¹ × 5⁴, 3 is in odd power. Therefore, the square root of 7500 is irrational.

If the Square Root of 7500 is 86.603. Find the Value of the Square Root of 75.

Let us represent √75 in p/q form i.e. √(7500/100) = 75/10 = 8.660. Hence, the value of √75.0 = 8.660

Is the number 7500 a Perfect Square?

The prime factorization of 7500 = 2² × 3¹ × 5⁴. Here, the prime factor 3 is not in the pair. Therefore, 7500 is not a perfect square.

What is the Value of 13 square root 7500?

The square root of 7500 is 86.603. Therefore, 13 √7500 = 13 × 86.603 = 1125.833.

What is the Square of the Square Root of 7500?

The square of the square root of 7500 is the number 7500 itself i.e. (√7500)² = (7500)^2/2 = 7500.

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