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Square roots have some useful properties that make calculations easier. One of the key properties is how square roots multiply.
Here it is: if you multiply the square root of a number by itself, you get that number. Written mathematically, it looks like this: \( \sqrt{a} \cdot \sqrt{a} = a \).
This property is very handy, especially when solving algebraic equations involving square roots.
So, in our exercise where we have \( \sqrt{17} \cdot \sqrt{17} \), we use this property to directly find the answer is 17.
Simple, right? Understanding this makes handling square roots far less complicated.

Simplifying radicals, or square roots, is a process you’ll use often in math. A radical like \( \sqrt{a} \) often looks simpler when you know how to simplify it.
But, what does that mean? Simplifying radicals usually means reducing them to their simplest form.
For instance, let’s say we have \( \sqrt{36} \). We know that 36 is a perfect square (as it equals 6*6), so \( \sqrt{36} = 6 \).
With non-perfect squares, you break them down into smaller factors. For example, take \( \sqrt{20} \). We can write 20 as 4*5. Because 4 is a perfect square, this becomes \( \sqrt{4} \cdot \sqrt{5} = 2 \cdot \sqrt{5} \).
Simplified forms of radicals can make further mathematical operations more manageable.

Algebraic multiplication involves multiplying terms, which often include numbers, variables, and occasionally square roots.
When it comes to multiplying square roots, the process aligns closely with general multiplication rules.
Consider the simple example in our exercise: \( \sqrt{17} \cdot \sqrt{17} \). We use the multiplication property for square roots: \( \sqrt{a} \cdot \sqrt{a} = a \).
Essentially, you're taking each square root and multiplying them together. The square root symbol effectively ‘cancels out,’ and you’re left with the number under the square root.
This straightforward multiplication rule simplifies many algebraic problems involving square roots.
So always remember: multiply the square roots, then apply the properties you know.