Square root of 150 in radical form
Understand the Problem
The question is asking for the square root of 150 expressed in radical form. To solve it, we will break down 150 into its prime factors to simplify the square root.
Answer
The square root of 150 expressed in radical form is $5\sqrt{6}$.
Answer for screen readers
The square root of 150 expressed in radical form is $5\sqrt{6}$.
Steps to Solve
- Factor 150 into Prime Factors
Start by finding the prime factors of 150.
150 can be divided by 2 (the smallest prime number): $$ 150 \div 2 = 75 $$
Next, factor 75: $$ 75 \div 3 = 25 $$
Now factor 25: $$ 25 = 5 \times 5 $$
Putting it all together, the prime factorization is: $$ 150 = 2 \times 3 \times 5^2 $$
- Apply the Square Root to Each Factor
Next, apply the square root to the entire prime factorization: $$ \sqrt{150} = \sqrt{2 \times 3 \times 5^2} $$
- Simplify the Square Root
Now, we can simplify the square root: $$ \sqrt{150} = \sqrt{2} \times \sqrt{3} \times \sqrt{5^2} $$
Since $ \sqrt{5^2} = 5$, we get: $$ \sqrt{150} = \sqrt{2} \times \sqrt{3} \times 5 $$
- Combine the Results
The simplified form can be arranged as: $$ \sqrt{150} = 5\sqrt{6} $$
The square root of 150 expressed in radical form is $5\sqrt{6}$.
More Information
The square root of 150 cannot be simplified into a whole number, but it can be expressed in radical form as $5\sqrt{6}$. This indicates that 150 can be broken down into components that include a perfect square, which aids in simplification.
Tips
- Mixing up the order of operations when breaking down the square root. Always remember to factor first before applying the square root.
- Forgetting to simplify completely once the square root is extracted. Ensure all perfect squares are accounted for in the final expression.
