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Square Root of 961

The square root of 961 is expressed as √961 in the radical form and as (961)^½ or (961)^0.5 in the exponent form. The square root of 961 is 31. It is the positive solution of the equation x² = 961. The number 961 is a perfect square.

Square Root of 961: 31
Square Root of 961 in exponential form: (961)^½ or (961)^0.5
Square Root of 961 in radical form: √961

Square Root of 961

1.	What is the Square Root of 961?
2.	How to find the Square Root of 961?
3.	Is the Square Root of 961 Rational?
4.	FAQs

What is the Square Root of 961?

The square root of 961, (or root 961), is the number which when multiplied by itself gives the product as 961. Therefore, the square root of 961 = √961 = 31.

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How to Find Square Root of 961?

Square Root of 961 by Long Division Method

Value of √961 by Long Division Method

Explanation:

Forming pairs: 09 and 61
Find a number Y (3) such that whose square is <= 9. Now divide 09 by 3 with quotient as 3.
Bring down the next pair 61, to the right of the remainder 0. The new dividend is now 61.
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 1) such that 6Z × Z <= 61. After finding Z, together 6 and Z (1) form a new divisor 61 for the new dividend 61.
Divide 61 by 61 with the quotient as 1, giving the remainder = 61 - 61 × 1 = 61 - 61 = 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 961 by long division method is 31.

Is Square Root of 961 Rational?

The value of √961 is 31. Hence, the square root of 961 is a rational number.

☛ Also Check:

Square Root of 80 - √80 = 8.94427
Square Root of 192 - √192 = 13.85641
Square Root of 225 - √225 = 15
Square Root of 13 - √13 = 3.60555
Square Root of 85 - √85 = 9.21954
Square Root of 25 - √25 = 5
Square Root of 8 - √8 = 2.82843

Square Root of 961 Solved Examples

Example 1: Solve the equation x² − 961 = 0

Solution:

x² - 961 = 0 i.e. x² = 961
x = ±√961
Since the value of the square root of 961 is 31,
⇒ x = +√961 or -√961 = 31 or -31.
Example 2: If the area of an equilateral triangle is 961√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 = 961√3 in²
⇒ a = ±√3844 in
Since length can't be negative,
⇒ a = √3844 = 2 √961
We know that the square root of 961 is 31.
⇒ a = 62 in
Example 3: If the area of a circle is 961π in². Find the radius of the circle.

Solution:

Let 'r' be the radius of the circle.
⇒ Area of the circle = πr² = 961π in²
⇒ r = ±√961 in
Since radius can't be negative,
⇒ r = √961
Square root of 961 is 31.
⇒ r = 31 in

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FAQs on the Square Root of 961

What is the Value of the Square Root of 961?

The square root of 961 is 31.

Why is the Square Root of 961 a Rational Number?

Upon prime factorizing 961 i.e. 31², we find that all the prime factors are in even power. This implies that the square root of 961 is a positive integer. Therefore, the square root of 961 is rational.

What is the Square Root of -961?

The square root of -961 is an imaginary number. It can be written as √-961 = √-1 × √961 = i √961 = 31i
where i = √-1 and it is called the imaginary unit.

If the Square Root of 961 is 31. Find the Value of the Square Root of 9.61.

Let us represent √9.61 in p/q form i.e. √(961/100) = 9.61/10 = 3. Hence, the value of √9.61 = 3

What is the Square Root of 961 in Simplest Radical Form?

We need to express 961 as the product of its prime factors i.e. 961 = 31 × 31 . Therefore, as visible, the radical form of the square root of 961 cannot be simplified further. Therefore, in the simplest radical form of the square root of 961 can be written as √961.

Evaluate 5 plus 10 square root 961

The given expression is 5 + 10 √961. We know that the square root of 961 is 31. Therefore, 5 + 10 √961 = 5 + 10 × 31 = 5 + 310 = 315

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