Square root of 50 simplified radical form
Understand the Problem
The question is asking for the simplified radical form of the square root of 50. To simplify, we can factor 50 into its prime factors and look for perfect squares.
Answer
$5\sqrt{2}$
Answer for screen readers
The simplified radical form of the square root of 50 is $5\sqrt{2}$.
Steps to Solve
- Factor 50 into Prime Factors
Start by factoring 50. We can do this as follows: $$ 50 = 2 \times 25 $$ Next, we can factor 25 into: $$ 25 = 5 \times 5 $$ So, the complete factorization of 50 is: $$ 50 = 2 \times 5^2 $$
- Identify Perfect Squares
Next, we identify any perfect squares within the factors. The perfect square here is $5^2$.
- Apply the Square Root Property
Using the square root property that states $\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$, we apply it to the factors of 50: $$ \sqrt{50} = \sqrt{2 \times 5^2} = \sqrt{2} \times \sqrt{5^2} $$
- Simplify the Expression
Since $\sqrt{5^2} = 5$, we can simplify this further: $$ \sqrt{50} = \sqrt{2} \times 5 $$ Thus, we have: $$ \sqrt{50} = 5\sqrt{2} $$
The simplified radical form of the square root of 50 is $5\sqrt{2}$.
More Information
Simplifying square roots is an essential skill in algebra. The process of factoring helps to identify perfect squares, which allows for more straightforward computation by removing the square root from those terms.
Tips
- Forgetting to look for all prime factors can lead to an incomplete simplification.
- Misidentifying perfect squares or skipping the simplification step can result in retaining unnecessary square roots.
