Square root of 242 simplified
Understand the Problem
The question is asking us to simplify the square root of 242, which involves finding the prime factors of 242 to express the square root in a simpler form.
Answer
$11\sqrt{2}$
Answer for screen readers
The simplified form of $\sqrt{242}$ is $11\sqrt{2}$.
Steps to Solve
- Find the prime factorization of 242
To simplify the square root, we first need to find the prime factors of 242. We can start by dividing by the smallest prime number, which is 2. $$ 242 \div 2 = 121 $$ Next, we factor 121. We can divide by 11 (which is also prime): $$ 121 \div 11 = 11 $$ So, we can express 242 as: $$ 242 = 2 \times 11^2 $$
- Write the square root in terms of its factors
Now, we can write the square root of 242 using its prime factors: $$ \sqrt{242} = \sqrt{2 \times 11^2} $$
- Simplify the square root
We can simplify this expression by taking the square root of $11^2$. Recall that $\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$: $$ \sqrt{242} = \sqrt{2} \times \sqrt{11^2} = \sqrt{2} \times 11 = 11\sqrt{2} $$
The simplified form of $\sqrt{242}$ is $11\sqrt{2}$.
More Information
The process of simplifying square roots involves prime factorization, allowing us to simplify expressions more effectively. Recognizing perfect squares, like $11^2$, helps in simplifying square roots.
Tips
One common mistake is stopping at the factorization and not recognizing that $11^2$ can be simplified out of the square root. Ensuring that the square roots of perfect squares are taken will help avoid this.
