Square Root of 1/4

The square root is the inverse of the square of a number. 1/4 is a perfect square. The square root of 1/4 is expressed in both radical and exponential form. In the radical form, it is expressed as √(1/4), whereas (1/4)^(1/2) in the exponential form. √(1/4) = 1/2, 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 process of finding square roots can vary depending on whether the number is a perfect square or not. For 1/4, which is a perfect square, simple arithmetic can be used. Let us now explore the following methods:

• Arithmetic method
• Prime factorization method
• Long division method

Since 1/4 is a perfect square, we can find its square root using simple arithmetic. The square root of a fraction is the square root of the numerator divided by the square root of the denominator.

Step 1: The numerator is 1, and the square root of 1 is 1.

Step 2: The denominator is 4, and the square root of 4 is 2.

Step 3: Therefore, the square root of 1/4 is 1/2.

The prime factorization method can be used to understand the structure of a number, even though it is not necessary for simple fractions like 1/4.

Step 1: The prime factorization of 1 is trivial as it is self-contained, and 4 can be expressed as 2 x 2.

Step 2: To find the square root, we pair the prime factors of the denominator. Since 4 = 2 x 2, its square root is 2.

Step 3: The square root of 1 is 1, so the square root of 1/4 is 1/2.

While the long division method is typically used for more complex numbers, it can also be applied here to illustrate the process.

Step 1: The fraction 1/4 can be converted to a decimal, 0.25.

Step 2: Use the long division method to find the square root of 0.25.

Step 3: Pair 25 as 0.25 and find a number whose square is close to 25.

Step 4: The number is 5 because 5 x 5 = 25.

Step 5: Therefore, the square root of 0.25 is 0.5, which corresponds to 1/2 in fractional form.

• Square root: A square root is a value that, when multiplied by itself, gives the original number. For example, the square root of 1/4 is 1/2.

• Rational number: A rational number is a number that can be expressed as the quotient or fraction p/q of two integers, where q ≠ 0.

• Perfect square: A perfect square is a number that is the square of an integer. For example, 1/4 is a perfect square because it is the square of 1/2.

• Fraction: A fraction represents a part of a whole or any number of equal parts, typically expressed as "a/b" where "a" is the numerator and "b" is the denominator.

• Decimal: A decimal is a fraction expressed in a special form, where the denominator is a power of ten. For example, 1/4 is equivalent to 0.25 in decimal form.