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Square Root of 1252

The square root of 1252 is expressed as √1252 in the radical form and as (1252)^½ or (1252)^0.5 in the exponent form. The square root of 1252 rounded up to 7 decimal places is 35.3836120. It is the positive solution of the equation x² = 1252. We can express the square root of 1252 in its lowest radical form as 2 √313.

Square Root of 1252: 35.38361202590826
Square Root of 1252 in exponential form: (1252)^½ or (1252)^0.5
Square Root of 1252 in radical form: √1252 or 2 √313

Square Root of 1252

1.	What is the Square Root of 1252?
2.	How to find the Square Root of 1252?
3.	Is the Square Root of 1252 Irrational?
4.	FAQs

What is the Square Root of 1252?

The square root of 1252, (or root 1252), is the number which when multiplied by itself gives the product as 1252. Therefore, the square root of 1252 = √1252 = 2 √313 = 35.38361202590826.

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How to Find Square Root of 1252?

Square Root of 1252 by Long Division Method

Value of √1252 by Long Division Method

Explanation:

Forming pairs: 12 and 52
Find a number Y (3) such that whose square is <= 12. Now divide 12 by 3 with quotient as 3.
Bring down the next pair 52, to the right of the remainder 3. The new dividend is now 352.
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 5) such that 6Z × Z <= 352. After finding Z, together 6 and Z (5) form a new divisor 65 for the new dividend 352.
Divide 352 by 65 with the quotient as 5, giving the remainder = 352 - 65 × 5 = 352 - 325 = 27.
Now, let's find the decimal places after the quotient 35.
Bring down 00 to the right of this remainder 27. The new dividend is now 2700.
Add the last digit of quotient to divisor i.e. 5 + 65 = 70. To the right of 70, find a digit Z (which is 3) such that 70Z × Z <= 2700. Together they form a new divisor (703) for the new dividend (2700).
Divide 2700 by 703 with the quotient as 3, giving the remainder = 2700 - 703 × 3 = 2700 - 2109 = 591.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 1252.

Therefore, the square root of 1252 by long division method is 35.3 approx.

Is Square Root of 1252 Irrational?

The actual value of √1252 is undetermined. The value of √1252 up to 25 decimal places is 35.38361202590826509358007. Hence, the square root of 1252 is an irrational number.

☛ Also Check:

Square Root of 169 - √169 = 13
Square Root of 120 - √120 = 10.95445
Square Root of 76 - √76 = 8.71780
Square Root of 34 - √34 = 5.83095
Square Root of 10 - √10 = 3.16228
Square Root of 48 - √48 = 6.92820
Square Root of 1024 - √1024 = 32

Square Root of 1252 Solved Examples

Example 1: Solve the equation x² − 1252 = 0

Solution:

x² - 1252 = 0 i.e. x² = 1252
x = ±√1252
Since the value of the square root of 1252 is 35.384,
⇒ x = +√1252 or -√1252 = 35.384 or -35.384.
Example 2: If the area of a circle is 1252π in². Find the radius of the circle.

Solution:

Let 'r' be the radius of the circle.
⇒ Area of the circle = πr² = 1252π in²
⇒ r = ±√1252 in
Since radius can't be negative,
⇒ r = √1252
The square root of 1252 is 35.384.
⇒ r = 35.384 in
Example 3: If the area of an equilateral triangle is 1252√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 = 1252√3 in²
⇒ a = ±√5008 in
Since length can't be negative,
⇒ a = √5008 = 2 √1252
We know that the square root of 1252 is 35.384.
⇒ a = 70.767 in

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FAQs on the Square Root of 1252

What is the Value of the Square Root of 1252?

The square root of 1252 is 35.38361.

Why is the Square Root of 1252 an Irrational Number?

Upon prime factorizing 1252 i.e. 2² × 313¹, 313 is in odd power. Therefore, the square root of 1252 is irrational.

What is the Square Root of 1252 in Simplest Radical Form?

We need to express 1252 as the product of its prime factors i.e. 1252 = 2 × 2 × 313. Therefore, √1252 = √2 × 2 × 313 = 2 √313. Thus, the square root of 1252 in the lowest radical form is 2 √313.

Is the number 1252 a Perfect Square?

The prime factorization of 1252 = 2² × 313¹. Here, the prime factor 313 is not in the pair. Therefore, 1252 is not a perfect square.

Evaluate 8 plus 6 square root 1252

The given expression is 8 + 6 √1252. We know that the square root of 1252 is 35.384. Therefore, 8 + 6 √1252 = 8 + 6 × 35.384 = 8 + 212.302 = 220.302

What is the Value of 16 square root 1252?

The square root of 1252 is 35.384. Therefore, 16 √1252 = 16 × 35.384 = 566.138.

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