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Square Root of 3721

The square root of 3721 is expressed as √3721 in the radical form and as (3721)^½ or (3721)^0.5 in the exponent form. The square root of 3721 is 61. It is the positive solution of the equation x² = 3721. The number 3721 is a perfect square.

Square Root of 3721: 61
Square Root of 3721 in exponential form: (3721)^½ or (3721)^0.5
Square Root of 3721 in radical form: √3721

Square Root of 3721

1.	What is the Square Root of 3721?
2.	How to find the Square Root of 3721?
3.	Is the Square Root of 3721 Rational?
4.	FAQs

What is the Square Root of 3721?

The square root of 3721, (or root 3721), is the number which when multiplied by itself gives the product as 3721. Therefore, the square root of 3721 = √3721 = 61.

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How to Find Square Root of 3721?

Square Root of 3721 by Long Division Method

Value of √3721 by Long Division Method

Explanation:

Forming pairs: 37 and 21
Find a number Y (6) such that whose square is <= 37. Now divide 37 by 6 with quotient as 6.
Bring down the next pair 21, to the right of the remainder 1. The new dividend is now 121.
Add the last digit of the quotient (6) to the divisor (6) i.e. 6 + 6 = 12. To the right of 12, find a digit Z (which is 1) such that 12Z × Z <= 121. After finding Z, together 12 and Z (1) form a new divisor 121 for the new dividend 121.
Divide 121 by 121 with the quotient as 1, giving the remainder = 121 - 121 × 1 = 121 - 121 = 0.
We stop the process since the remainder is now 0 and there are no more digits that can be brought down.

Therefore, the square root of 3721 by long division method is 61.

Is Square Root of 3721 Rational?

The value of √3721 is 61. Hence, the square root of 3721 is a rational number.

☛ Also Check:

Square Root of 89 - √89 = 9.43398
Square Root of 97 - √97 = 9.84886
Square Root of 42 - √42 = 6.48074
Square Root of 56 - √56 = 7.48331
Square Root of 36 - √36 = 6
Square Root of 106 - √106 = 10.29563
Square Root of 92 - √92 = 9.59166

Square Root of 3721 Solved Examples

Example 1: Solve the equation x² − 3721 = 0

Solution:

x² - 3721 = 0 i.e. x² = 3721
x = ±√3721
Since the value of the square root of 3721 is 61,
⇒ x = +√3721 or -√3721 = 61 or -61.
Example 2: If the area of a circle is 3721π in². Find the radius of the circle.

Solution:

Let 'r' be the radius of the circle.
⇒ Area of the circle = πr² = 3721π in²
⇒ r = ±√3721 in
Since radius can't be negative,
⇒ r = √3721
Square root of 3721 is 61.
⇒ r = 61 in
Example 3: If the area of an equilateral triangle is 3721√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 = 3721√3 in²
⇒ a = ±√14884 in
Since length can't be negative,
⇒ a = √14884 = 2 √3721
We know that the square root of 3721 is 61.
⇒ a = 122 in

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FAQs on the Square Root of 3721

What is the Value of the Square Root of 3721?

The square root of 3721 is 61.

Why is the Square Root of 3721 a Rational Number?

Upon prime factorizing 3721 i.e. 61², we find that all the prime factors are in even power. This implies that the square root of 3721 is a positive integer. Therefore, the square root of 3721 is rational.

What is the Square of the Square Root of 3721?

The square of the square root of 3721 is the number 3721 itself i.e. (√3721)² = (3721)^2/2 = 3721.

If the Square Root of 3721 is 61. Find the Value of the Square Root of 37.21.

Let us represent √37.21 in p/q form i.e. √(3721/100) = 37.21/10 = 6. Hence, the value of √37.21 = 6

Is the number 3721 a Perfect Square?

The prime factorization of 3721 = 61². Here, all the numbers are in the power of 2. This implies that the square root of 3721 is a positive integer. Therefore, 3721 is a perfect square.

Evaluate 13 plus 13 square root 3721

The given expression is 13 + 13 √3721. We know that the square root of 3721 is 61. Therefore, 13 + 13 √3721 = 13 + 13 × 61 = 13 + 793 = 806

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