Multiplying square roots can seem tricky at first, but it’s quite straightforward once you understand the basic principles involved. Here’s a step-by-step guide on how to do it:
Step 1: Understand the Property of Square Roots
The key property that you need to know is that the square root of a product is equal to the product of the square roots. Mathematically, this is expressed as:
√(a * b) = √a * √b
Step 2: Multiply the Numbers Inside the Square Roots
When you want to multiply two square roots, you can simply multiply the numbers under the square root signs together. For example, if you’re multiplying √2 and √3, you can write:
√2 * √3 = √(2 * 3) = √6
Step 3: Simplify if Possible
In some cases, the result under the square root can be simplified. For example:
If you multiply √8 and √2, you get:
√8 * √2 = √(8 * 2) = √16
Since √16 equals 4, you’ve found a simpler form.
Step 4: Combine Like Terms
If you find that the square roots share common factors or you need to simplify further, you can factor out perfect squares. Let’s say you have:
√12 * √3
You can simplify √12 first:
√12 = √(4 * 3) = √4 * √3 = 2√3
So now,:
√12 * √3 = (2√3) * √3 = 2 * 3 = 6
Example Problem:
Let’s put this into practice with an example. Suppose you want to multiply √5 and √20:
√5 * √20 = √(5 * 20) = √100 = 10
In summary, multiplying square roots involves multiplying the numbers under the roots and then simplifying when possible. Just remember that taking the square root of a product can make calculations much easier!