Square root of a product

🏆Practice the root of a product

The square root of a product

When we encounter a root that encompasses the entirety of the product, we can decompose the factors of the products and leave a separate root for each of them. Let's not forget to leave the multiplication sign between the factors we have extracted.

Let's put it this way:
(ab)=ab\sqrt{(a\cdot b)}=\sqrt{a}\cdot\sqrt{b}

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Test yourself on the root of a product!


Solve the following exercise:

\( \sqrt{30}\cdot\sqrt{1}= \)

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Let's look at this in the example

According to the rule of the root of a product, we can break down the factors and leave the root of each factor separately while maintaining the multiplication operation between them:
We will break it down and obtain:

If you are interested in this article, you might also be interested in the following articles:

Laws of Radicals

Root of the Quotient


Combining Powers and Roots

In the blog of Tutorela you will find a variety of articles about mathematics.

Examples and exercises with solutions of the root of a product


Given the following rectangle:


Given ΔAEB isosceles (AE=EB).

Find the perimeter of the rectangle ABCD.



8+163 8+16\sqrt3

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