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Square Root of 507

The square root of 507 is expressed as √507 in the radical form and as (507)^½ or (507)^0.5 in the exponent form. The square root of 507 rounded up to 7 decimal places is 22.5166605. It is the positive solution of the equation x² = 507. We can express the square root of 507 in its lowest radical form as 13 √3.

Square Root of 507: 22.516660498395403
Square Root of 507 in exponential form: (507)^½ or (507)^0.5
Square Root of 507 in radical form: √507 or 13 √3

Square Root of 507

1.	What is the Square Root of 507?
2.	How to find the Square Root of 507?
3.	Is the Square Root of 507 Irrational?
4.	FAQs

What is the Square Root of 507?

The square root of 507, (or root 507), is the number which when multiplied by itself gives the product as 507. Therefore, the square root of 507 = √507 = 13 √3 = 22.516660498395403.

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How to Find Square Root of 507?

Square Root of 507 by Long Division Method

Value of √507 by Long Division Method

Explanation:

Forming pairs: 05 and 07
Find a number Y (2) such that whose square is <= 5. Now divide 05 by 2 with quotient as 2.
Bring down the next pair 07, to the right of the remainder 1. The new dividend is now 107.
Add the last digit of the quotient (2) to the divisor (2) i.e. 2 + 2 = 4. To the right of 4, find a digit Z (which is 2) such that 4Z × Z <= 107. After finding Z, together 4 and Z (2) form a new divisor 42 for the new dividend 107.
Divide 107 by 42 with the quotient as 2, giving the remainder = 107 - 42 × 2 = 107 - 84 = 23.
Now, let's find the decimal places after the quotient 22.
Bring down 00 to the right of this remainder 23. The new dividend is now 2300.
Add the last digit of quotient to divisor i.e. 2 + 42 = 44. To the right of 44, find a digit Z (which is 5) such that 44Z × Z <= 2300. Together they form a new divisor (445) for the new dividend (2300).
Divide 2300 by 445 with the quotient as 5, giving the remainder = 2300 - 445 × 5 = 2300 - 2225 = 75.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 507.

Therefore, the square root of 507 by long division method is 22.5 approx.

Is Square Root of 507 Irrational?

The actual value of √507 is undetermined. The value of √507 up to 25 decimal places is 22.51666049839540481585680. Hence, the square root of 507 is an irrational number.

☛ Also Check:

Square Root of 44 - √44 = 6.63325
Square Root of 21 - √21 = 4.58258
Square Root of 140 - √140 = 11.83216
Square Root of 324 - √324 = 18
Square Root of 1000 - √1000 = 31.62278
Square Root of 105 - √105 = 10.24695
Square Root of 13 - √13 = 3.60555

Square Root of 507 Solved Examples

Example 1: Solve the equation x² − 507 = 0

Solution:

x² - 507 = 0 i.e. x² = 507
x = ±√507
Since the value of the square root of 507 is 22.517,
⇒ x = +√507 or -√507 = 22.517 or -22.517.
Example 2: If the area of a circle is 507π in². Find the radius of the circle.

Solution:

Let 'r' be the radius of the circle.
⇒ Area of the circle = πr² = 507π in²
⇒ r = ±√507 in
Since radius can't be negative,
⇒ r = √507
The square root of 507 is 22.517.
⇒ r = 22.517 in
Example 3: If the area of an equilateral triangle is 507√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 = 507√3 in²
⇒ a = ±√2028 in
Since length can't be negative,
⇒ a = √2028 = 2 √507
We know that the square root of 507 is 22.517.
⇒ a = 45.033 in

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FAQs on the Square Root of 507

What is the Value of the Square Root of 507?

The square root of 507 is 22.51666.

Why is the Square Root of 507 an Irrational Number?

Upon prime factorizing 507 i.e. 3¹ × 13², 3 is in odd power. Therefore, the square root of 507 is irrational.

Evaluate 16 plus 20 square root 507

The given expression is 16 + 20 √507. We know that the square root of 507 is 22.517. Therefore, 16 + 20 √507 = 16 + 20 × 22.517 = 16 + 450.333 = 466.333

What is the Square of the Square Root of 507?

The square of the square root of 507 is the number 507 itself i.e. (√507)² = (507)^2/2 = 507.

Is the number 507 a Perfect Square?

The prime factorization of 507 = 3¹ × 13². Here, the prime factor 3 is not in the pair. Therefore, 507 is not a perfect square.

If the Square Root of 507 is 22.517. Find the Value of the Square Root of 5.07.

Let us represent √5.07 in p/q form i.e. √(507/100) = 5.07/10 = 2.252. Hence, the value of √5.07 = 2.252

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