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Square Root of 1125

The square root of 1125 is expressed as √1125 in the radical form and as (1125)^½ or (1125)^0.5 in the exponent form. The square root of 1125 rounded up to 9 decimal places is 33.541019662. It is the positive solution of the equation x² = 1125. We can express the square root of 1125 in its lowest radical form as 15 √5.

Square Root of 1125: 33.54101966249684
Square Root of 1125 in exponential form: (1125)^½ or (1125)^0.5
Square Root of 1125 in radical form: √1125 or 15 √5

Square Root of 1125

1.	What is the Square Root of 1125?
2.	How to find the Square Root of 1125?
3.	Is the Square Root of 1125 Irrational?
4.	FAQs

What is the Square Root of 1125?

The square root of 1125, (or root 1125), is the number which when multiplied by itself gives the product as 1125. Therefore, the square root of 1125 = √1125 = 15 √5 = 33.54101966249684.

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How to Find Square Root of 1125?

Square Root of 1125 by Long Division Method

Value of √1125 by Long Division Method

Explanation:

Forming pairs: 11 and 25
Find a number Y (3) such that whose square is <= 11. Now divide 11 by 3 with quotient as 3.
Bring down the next pair 25, to the right of the remainder 2. The new dividend is now 225.
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 3) such that 6Z × Z <= 225. After finding Z, together 6 and Z (3) form a new divisor 63 for the new dividend 225.
Divide 225 by 63 with the quotient as 3, giving the remainder = 225 - 63 × 3 = 225 - 189 = 36.
Now, let's find the decimal places after the quotient 33.
Bring down 00 to the right of this remainder 36. The new dividend is now 3600.
Add the last digit of quotient to divisor i.e. 3 + 63 = 66. To the right of 66, find a digit Z (which is 5) such that 66Z × Z <= 3600. Together they form a new divisor (665) for the new dividend (3600).
Divide 3600 by 665 with the quotient as 5, giving the remainder = 3600 - 665 × 5 = 3600 - 3325 = 275.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 1125.

Therefore, the square root of 1125 by long division method is 33.5 approximately.

Is Square Root of 1125 Irrational?

The actual value of √1125 is undetermined. The value of √1125 up to 25 decimal places is 33.54101966249684544613761. Hence, the square root of 1125 is an irrational number.

☛ Also Check:

Square Root of 1000 - √1000 = 31.62278
Square Root of 76 - √76 = 8.71780
Square Root of 16 - √16 = 4
Square Root of 1521 - √1521 = 39
Square Root of 85 - √85 = 9.21954
Square Root of 784 - √784 = 28
Square Root of 14 - √14 = 3.74166

Square Root of 1125 Solved Examples

Example 1: Solve the equation x² − 1125 = 0

Solution:

x² - 1125 = 0 i.e. x² = 1125
x = ±√1125
Since the value of the square root of 1125 is 33.541,
⇒ x = +√1125 or -√1125 = 33.541 or -33.541.
Example 2: If the surface area of a cube is 6750 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 = 6750 in²
⇒ a = ±√1125 in
Since length can't be negative,
⇒ a = √1125
We know that the square root of 1125 is 33.541.
⇒ a = 33.541 in
Example 3: If the area of an equilateral triangle is 1125√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 = 1125√3 in²
⇒ a = ±√4500 in
Since length can't be negative,
⇒ a = √4500 = 2 √1125
We know that the square root of 1125 is 33.541.
⇒ a = 67.082 in

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FAQs on the Square Root of 1125

What is the Value of the Square Root of 1125?

The square root of 1125 is 33.54101.

Why is the Square Root of 1125 an Irrational Number?

Upon prime factorizing 1125 i.e. 3² × 5³, 5 is in odd power. Therefore, the square root of 1125 is irrational.

What is the Square Root of 1125 in Simplest Radical Form?

We need to express 1125 as the product of its prime factors i.e. 1125 = 3 × 3 × 5 × 5 × 5. Therefore, √1125 = √3 × 3 × 5 × 5 × 5 = 15 √5. Thus, the square root of 1125 in the lowest radical form is 15 √5.

What is the Square of the Square Root of 1125?

The square of the square root of 1125 is the number 1125 itself i.e. (√1125)² = (1125)^2/2 = 1125.

Is the number 1125 a Perfect Square?

The prime factorization of 1125 = 3² × 5³. Here, the prime factor 5 is not in the pair. Therefore, 1125 is not a perfect square.

What is the Square Root of -1125?

The square root of -1125 is an imaginary number. It can be written as √-1125 = √-1 × √1125 = i √1125 = 33.541i
where i = √-1 and it is called the imaginary unit.

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