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Square Root of 1525

The square root of 1525 is expressed as √1525 in the radical form and as (1525)^½ or (1525)^0.5 in the exponent form. The square root of 1525 rounded up to 6 decimal places is 39.051248. It is the positive solution of the equation x² = 1525. We can express the square root of 1525 in its lowest radical form as 5 √61.

Square Root of 1525: 39.05124837953327
Square Root of 1525 in exponential form: (1525)^½ or (1525)^0.5
Square Root of 1525 in radical form: √1525 or 5 √61

Square Root of 1525

1.	What is the Square Root of 1525?
2.	How to find the Square Root of 1525?
3.	Is the Square Root of 1525 Irrational?
4.	FAQs

What is the Square Root of 1525?

The square root of 1525, (or root 1525), is the number which when multiplied by itself gives the product as 1525. Therefore, the square root of 1525 = √1525 = 5 √61 = 39.05124837953327.

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How to Find Square Root of 1525?

Square Root of 1525 by Long Division Method

Value of √1525 by Long Division Method

Explanation:

Forming pairs: 15 and 25
Find a number Y (3) such that whose square is <= 15. Now divide 15 by 3 with quotient as 3.
Bring down the next pair 25, to the right of the remainder 6. The new dividend is now 625.
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 9) such that 6Z × Z <= 625. After finding Z, together 6 and Z (9) form a new divisor 69 for the new dividend 625.
Divide 625 by 69 with the quotient as 9, giving the remainder = 625 - 69 × 9 = 625 - 621 = 4.
Now, let's find the decimal places after the quotient 39.
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. 9 + 69 = 78. To the right of 78, find a digit Z (which is 0) such that 78Z × Z <= 400. Together they form a new divisor (780) for the new dividend (400).
Divide 400 by 780 with the quotient as 0, giving the remainder = 400 - 780 × 0 = 400 - 0 = 400.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 1525.

Therefore, the square root of 1525 by long division method is 39.0 approx.

Is Square Root of 1525 Irrational?

The actual value of √1525 is undetermined. The value of √1525 up to 25 decimal places is 39.05124837953327197064861. Hence, the square root of 1525 is an irrational number.

☛ Also Check:

Square Root of 40 - √40 = 6.32456
Square Root of 42 - √42 = 6.48074
Square Root of 900 - √900 = 30
Square Root of 11 - √11 = 3.31662
Square Root of 225 - √225 = 15
Square Root of 17 - √17 = 4.12311
Square Root of 33 - √33 = 5.74456

Square Root of 1525 Solved Examples

Example 1: Solve the equation x² − 1525 = 0

Solution:

x² - 1525 = 0 i.e. x² = 1525
x = ±√1525
Since the value of the square root of 1525 is 39.051,
⇒ x = +√1525 or -√1525 = 39.051 or -39.051.
Example 2: If the area of an equilateral triangle is 1525√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 = 1525√3 in²
⇒ a = ±√6100 in
Since length can't be negative,
⇒ a = √6100 = 2 √1525
We know that the square root of 1525 is 39.051.
⇒ a = 78.102 in
Example 3: If the surface area of a cube is 9150 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 = 9150 in²
⇒ a = ±√1525 in
Since length can't be negative,
⇒ a = √1525
We know that the square root of 1525 is 39.051.
⇒ a = 39.051 in

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FAQs on the Square Root of 1525

What is the Value of the Square Root of 1525?

The square root of 1525 is 39.05124.

Why is the Square Root of 1525 an Irrational Number?

Upon prime factorizing 1525 i.e. 5² × 61¹, 61 is in odd power. Therefore, the square root of 1525 is irrational.

What is the Value of 14 square root 1525?

The square root of 1525 is 39.051. Therefore, 14 √1525 = 14 × 39.051 = 546.717.

Evaluate 4 plus 12 square root 1525

The given expression is 4 + 12 √1525. We know that the square root of 1525 is 39.051. Therefore, 4 + 12 √1525 = 4 + 12 × 39.051 = 4 + 468.615 = 472.615

What is the Square Root of -1525?

The square root of -1525 is an imaginary number. It can be written as √-1525 = √-1 × √1525 = i √1525 = 39.051i
where i = √-1 and it is called the imaginary unit.

What is the Square Root of 1525 in Simplest Radical Form?

We need to express 1525 as the product of its prime factors i.e. 1525 = 5 × 5 × 61. Therefore, √1525 = √5 × 5 × 61 = 5 √61. Thus, the square root of 1525 in the lowest radical form is 5 √61.

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