Square Root Of 1 961

Square Root of 961

The square root of 961 is expressed equally √961 in the radical form and every bit (961)^½ or (961)^0.5 in the exponent form. The foursquare 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.v
Square Root of 961 in radical form: √961

Square Root of 961

1.	What is the Square Root of 961?
ii.	How to observe the Square Root of 961?
3.	Is the Foursquare 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 past Long Division Method

Explanation:

Forming pairs: 09 and 61
Find a number Y (3) such that whose square is <= 9. Now split up 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 ane) such that 6Z × Z <= 61. After finding Z, together 6 and Z (1) course a new divisor 61 for the new dividend 61.
Divide 61 by 61 with the caliber equally 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 than digits that can be brought downward.

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.

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Foursquare Root of 80 - √80 = eight.94427
Square Root of 192 - √192 = 13.85641
Square Root of 225 - √225 = 15
Square Root of 13 - √thirteen = 3.60555
Square Root of 85 - √85 = 9.21954
Square Root of 25 - √25 = 5
Square Root of viii - √viii = ii.82843

Square Root of 961 Solved Examples

Example one: Solve the equation 10² − 961 = 0

Solution:

x^two - 961 = 0 i.e. xⁱⁱ = 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 surface area of an equilateral triangle is 961√three in². Find the length of one of the sides of the triangle.

Solution:

Allow '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 iii: If the area of a circle is 961π inⁱⁱ. Find the radius of the circumvolve.

Solution:

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

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FAQs on the Foursquare 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 number factorizing 961 i.e. 31^two, nosotros detect that all the prime number factors are in fifty-fifty ability. This implies that the square root of 961 is a positive integer. Therefore, the foursquare 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 = √-one and it is called the imaginary unit of measurement.

If the Foursquare Root of 961 is 31. Find the Value of the Square Root of nine.61.

Let us represent √9.61 in p/q form i.due east. √(961/100) = nine.61/10 = 3. Hence, the value of √9.61 = 3

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

We demand to express 961 as the product of its prime factors i.eastward. 961 = 31 × 31 . Therefore, every bit visible, the radical form of the square root of 961 cannot exist simplified farther. Therefore, in the simplest radical form of the square root of 961 can exist written as √961.