Square Root of 16/100

The square root is the inverse of the square of the number. 16/100 is a perfect square fraction. The square root of 16/100 can be expressed in both radical and exponential form. In radical form, it is expressed as √(16/100), whereas in exponential form, it is expressed as (16/100)^(1/2). √(16/100) = √(4/10) = 2/10 = 0.2, 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 square root of a fraction is found by taking the square root of the numerator and the denominator separately. Let us now learn the method:

Step 1: Find the square root of the numerator (16) and the denominator (100).

Step 2: The square root of 16 is 4, and the square root of 100 is 10.

Step 3: So, the square root of 16/100 is 4/10, which simplifies to 0.2.

Prime factorization can also be used to find the square root of perfect square fractions.

Step 1: Find the prime factors of the numerator and denominator. The prime factors of 16 are 2 x 2 x 2 x 2, and the prime factors of 100 are 2 x 2 x 5 x 5.

Step 2: Pair the prime factors: Numerator: (2 x 2) x (2 x 2) Denominator: (2 x 2) x (5 x 5)

Step 3: Take one factor from each pair: Numerator: 2 x 2 = 4 Denominator: 2 x 5 = 10

Step 4: The square root of 16/100 is 4/10, which simplifies to 0.2.

The long division method is typically used for non-perfect squares, but it can confirm our results.

Step 1: Express 16/100 as a decimal, which is 0.16.

Step 2: Use long division to find the square root of 0.16.

Step 3: Since 0.16 is a perfect square, the square root is 0.4.

Step 4: Adjust for the initial fraction by dividing by 2 to get 0.2.

Approximation is useful for estimating square roots, especially when a fraction isn't a perfect square.

Step 1: Note that 16/100 is a perfect square, so approximation isn't necessary, but it's helpful to verify.

Step 2: Recognize that √(16/100) is between √(1/100) = 0.1 and √(25/100) = 0.5.

Step 3: Since 16 is a perfect square and so is 100, the exact answer is 0.2.

• Square root: The square root of a number is a value that, when multiplied by itself, gives the original number. Example: √16 = 4.

• Rational number: A rational number is a number that can be expressed as the quotient or fraction p/q of two integers, where q is not zero.

• Perfect square: A perfect square is a number that is the square of an integer. Example: 16 is a perfect square because 4 × 4 = 16.

• Fraction: A fraction represents a part of a whole or, more generally, any number of equal parts. It consists of a numerator and a denominator.

• Decimal: A decimal is a way of representing numbers that have a whole part and a fractional part, separated by a decimal point. Example: 0.2 is a decimal.