Pre-Algebra

sqrt(17/9)

Step-by-step solution with explanation

Final Answer

Step-by-step solution

1

Separate the square root as a fraction

A square root of a fraction equals the square root of the top divided by the square root of the bottom. This rule lets us simplify each part on its own.
2

Simplify the square root of 9

9 is a perfect square because 3 × 3 = 9. So the bottom becomes a clean whole number.
3

Check if square root of 17 simplifies

17 is a prime number, so it has no perfect square factors. The square root of 17 cannot be simplified further and stays as-is.
4

Write the final simplified form

We put together the simplified top and bottom. The exact answer is , and the decimal approximation is about 1.374.

Understanding this problem

Learning Insight

The rule works because squaring both sides gives , confirming they are equal. Splitting a fraction under a radical is a core simplification strategy — it turns one hard problem into two easier ones.

Quick Tip

Always check the bottom first. If the denominator is a perfect square (like 4, 9, 16, 25…), it simplifies to a whole number and cleans up the expression fast.

Common Mistake

Students often try to add or combine the numbers under the radical — for example writing as (forgetting to take the square root of the bottom) or misidentifying 17 as having a perfect square factor when it does not.