Simplify square root of 13.28/9

Solution:

Step 1:

Calculate the quotient of $13.28$ divided by $9$ to find the value under the square root. $\sqrt{\frac{13.28}{9}}$

Step 2:

Express the square root of the quotient in various representations. Exact Form: $\sqrt{\frac{13.28}{9}}$ Decimal Form: $1.21472447 \ldots$

Knowledge Notes:

To simplify the square root of a fraction, you follow these steps:

1. Division: Start by dividing the numerator by the denominator to obtain the value that will be under the square root.

2. Square Root Calculation: After division, you take the square root of the result. This can be done using a calculator for decimal approximations or by finding the square root in its simplest radical form if possible.

3. Representation: The result of a square root can be expressed in different forms:

   • Exact Form: This is the square root of the fraction in its simplest radical form, which may not always be possible for non-perfect squares.

   • Decimal Form: This is a numerical approximation of the square root, which is often represented by a decimal that may be rounded to a certain number of places or shown as a continuing decimal.

4. Simplifying Fractions: Before taking the square root, if the fraction can be simplified (i.e., both the numerator and denominator have a common factor), it should be done to make the calculation easier.

5. Rationalizing the Denominator: If the fraction under the square root has a radical in the denominator after simplification, the process of rationalization may be used to eliminate the radical from the denominator.

In this particular problem, since $13.28$ is a decimal and $9$ is a whole number, we directly divide and then take the square root of the quotient. The exact form of the square root of a non-perfect square is typically left under the radical sign, while the decimal form is an approximation.