Pre-Algebra

sqrt(605) / sqrt(5)

Step-by-step solution with explanation

Final Answer

Step-by-step solution

1

Combine radicals into one fraction

When you divide two square roots, you can write them as a single square root of the fraction. This makes the problem much easier to simplify.
2

Divide the numbers inside the radical

605 divided by 5 equals 121. Now we just need to find the square root of 121.
3

Take the square root of 121

11 times 11 equals 121, so the square root of 121 is exactly 11. This is a perfect square, so we get a clean whole number answer.

Understanding this problem

Learning Insight

The rule works because square roots and fractions both follow the same multiplication rules. Combining them first lets you simplify the numbers before dealing with the radical, which is almost always easier.

Quick Tip

Before doing anything else, always check if you can divide the numbers under the radicals. If the result is a perfect square (1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121…), you'll get a neat whole number answer.

Common Mistake

Students often try to simplify each square root separately — for example, trying to simplify alone — which leads to messy decimals or errors. Combining into one square root first avoids all that extra work.