sqrt 96 simplified
Understand the Problem
The question is asking for the simplified form of the square root of 96. To solve this, we will factor 96 into its prime factors and simplify the square root accordingly.
Answer
The simplified form of the square root of 96 is $4\sqrt{6}$.
Answer for screen readers
The simplified form of the square root of 96 is $4\sqrt{6}$.
Steps to Solve
- Factor the number 96 into its prime factors
Start by determining the prime factorization of 96. To do this, divide by the smallest prime numbers until you reach 1.
$$ 96 \div 2 = 48 \ 48 \div 2 = 24 \ 24 \div 2 = 12 \ 12 \div 2 = 6 \ 6 \div 2 = 3 \ 3 \div 3 = 1 $$
The prime factors of 96 are $2^5$ and $3^1$.
- Rewrite 96 using its prime factors
Now that we have the prime factorization, we write it as:
$$ 96 = 2^5 \times 3^1 $$
- Simplify the square root
Using the prime factorization, we find the square root:
$$ \sqrt{96} = \sqrt{2^5 \times 3^1} $$
We can separate the square root into two parts:
$$ \sqrt{96} = \sqrt{(2^4 \times 2^1) \times 3^1} = \sqrt{2^4} \times \sqrt{2^1} \times \sqrt{3^1} $$
Since $\sqrt{2^4} = 4$, we can continue simplifying:
$$ = 4 \times \sqrt{2} \times \sqrt{3} = 4 \times \sqrt{6} $$
So, the simplified form of $\sqrt{96}$ is:
$$ \sqrt{96} = 4 \sqrt{6} $$
The simplified form of the square root of 96 is $4\sqrt{6}$.
More Information
The process of simplifying square roots involves recognizing perfect squares within the number. In this example, $2^4$ is a perfect square (which equals 4 when taking the square root). This method can be applied to other square roots as well.
Tips
- Forgetting to include all prime factors when factoring a number.
- Miscalculation when finding square roots of the prime factors.
- Not simplifying the square root fully by leaving square roots intact.