Simplify square root of 96/2

The question is asking for the simplification of a mathematical expression involving a square root. The expression provided is the square root of 96 divided by 2. The task is to perform the necessary arithmetic operations and simplifications to express the result in a more simplified or reduced form, if possible. This typically would involve breaking down the square root into its prime factors and then simplifying by identifying perfect squares within that can be taken out of the square root as whole numbers.

$\sqrt{\frac{96}{2}}$

Answer

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Solution:

Step 1:

Calculate $\frac{96}{2}$ to get $\sqrt{48}$ .

Step 2:

Express $48$ as a product of its prime factors: $48 = 4^{2} \times 3$ .

Step 3:

Extract the square root of the perfect square from the radical: $\sqrt{16 \times 3}$ .

Step 4:

Recognize that $16$ is a perfect square and can be written as $4^{2}$ : $\sqrt{4^{2} \times 3}$ .

Step 5:

Simplify the square root by taking out the square term: $4 \sqrt{3}$ .

Step 6:

Present the simplified result in its exact and decimal forms:

Exact Form: $4 \sqrt{3}$
Decimal Form: Approximately $6.92820323$

Knowledge Notes:

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

Division before Square Root: If the numerator is divisible by the denominator, perform the division first to simplify the expression.
Prime Factorization: Break down the resulting number inside the square root into its prime factors to identify any perfect squares.
Extract Perfect Squares: Any perfect square factors can be taken out of the square root as their square root values.
Rewriting Perfect Squares: Recognize that numbers like $16$ can be written as $4^{2}$ , which helps in simplifying the square root.
Simplification: After extracting the perfect square, you will have the square root of a simpler expression, which may be a prime number or another integer.
Exact and Decimal Forms: The result can be expressed in its exact form involving square roots or approximated to a decimal using a calculator.

Relevant mathematical concepts include:

Square Roots: The square root of a number is a value that, when multiplied by itself, gives the original number.
Perfect Squares: Numbers like $4^{2} = 16$ are called perfect squares because their square roots are whole numbers.
Prime Factorization: This is the process of breaking down a composite number into a product of its prime factors.
Radicals: The symbol $\sqrt{}$ is used to denote the square root. Simplifying expressions under a radical often involves identifying and extracting perfect squares.
Decimal Approximation: Some square roots do not result in whole numbers and are instead irrational numbers. These can be approximated to decimal values for practical use.