Square Root of 1/961

The square root is the inverse of squaring a number. 1/961 is a fraction and can be considered a perfect square. The square root of 1/961 is expressed in both radical and exponential forms. In radical form, it is expressed as √(1/961), whereas in exponential form, it is (1/961)^(1/2). The square root of 1/961 is 1/31, which is a rational number because it can be expressed in the form of p/q, where p and q are integers and q ≠ 0.

The prime factorization method can be used for perfect squares, and since 1/961 can be broken down into perfect squares, it can be simplified easily. Let's learn the following methods:

• Prime factorization method
   
• Direct calculation

Prime factorization involves expressing a number as the product of its prime factors. Let's break down 961:

Step 1: Prime factorization of 961 Breaking it down, we get 31 x 31: 31^2

Step 2: Since 1/961 is 1/(31^2), the square root is 1/31. This is because the square root of a quotient is the quotient of the square roots.

For fractions like 1/961, the square root can be calculated directly:

Step 1: Recognize that 961 = 31^2.

Step 2: The square root of 1 is 1.

Step 3: Therefore, the square root of 1/961 is 1/31.

• Square root: A square root is the inverse of squaring a number. For example, 5² = 25, and the inverse is √25 = 5.

• Rational number: A rational number can be expressed in the form of p/q, where p and q are integers and q ≠ 0.

• Perfect square: A perfect square is a number that can be expressed as the square of an integer. For example, 961 is a perfect square (31²).

• Fraction: A fraction represents a part of a whole and is expressed as a ratio of two numbers, such as 1/31.

• Quotient: In division, the quotient is the result of dividing one number by another. For example, in 10 ÷ 2 = 5, the quotient is 5.