Write $6 \sqrt{20}$ in simple square root form.
$8 \sqrt{5}$
60
$30 \sqrt{4}$
$12 \sqrt{5}$
Answer (1)
Factor the number inside the square root: 20 = 2 2 × 5 .
Take the square root of the perfect square factor: 2 2 = 2 .
Multiply the number outside the square root: 6 × 2 = 12 .
Write the final expression in simple square root form: 12 5
Explanation
Understanding the Problem We are asked to write 6 20 in simple square root form. This means we want to express the given expression in the form a b , where b has no square factors other than 1. In other words, we want to simplify the square root as much as possible.
Factoring the Square Root First, we need to simplify the square root. We can factor 20 as 20 = 4 × 5 = 2 2 × 5 . Therefore, we can rewrite the original expression as: 6 20 = 6 2 2 × 5
Simplifying the Expression Now, we can take the square root of 2 2 , which is 2. So, we have: 6 2 2 × 5 = 6 × 2 5
Final Calculation Finally, we multiply the numbers outside the square root: 6 × 2 5 = 12 5 Thus, the simplified form of 6 20 is 12 5 .
Examples
Understanding how to simplify radicals is useful in many areas, such as calculating distances or areas. For example, if you are building a square garden with an area of 20 square feet, each side would be 20 feet long. Simplifying this gives 2 5 feet. Knowing this simplified form can help you better visualize and measure the garden's dimensions.
