To solve the problem of finding the product [tex]\(\sqrt{b} \cdot \sqrt{b}\)[/tex], let’s follow these steps:
1. Understand the roots:
The square root function, denoted as [tex]\(\sqrt{b}\)[/tex], is defined such that if [tex]\(x = \sqrt{b}\)[/tex], then [tex]\(x \cdot x = b\)[/tex]. This implies that the square root of a number, when multiplied by itself, returns the original number.
2. Product of the roots:
We are given the expression [tex]\(\sqrt{b} \cdot \sqrt{b}\)[/tex]. By the properties of square roots:
[tex]\[
\sqrt{b} \cdot \sqrt{b} = (\sqrt{b})^2
\][/tex]
3. Simplify the expression:
Using the property of exponents that [tex]\((\sqrt{b})^2 = b\)[/tex], we can simplify:
[tex]\[
(\sqrt{b})^2 = b
\][/tex]
4. Conclude the result:
Therefore, the product [tex]\(\sqrt{b} \cdot \sqrt{b}\)[/tex] simplifies to [tex]\(b\)[/tex].
Hence, the value of [tex]\(\sqrt{b} \cdot \sqrt{b}\)[/tex] is [tex]\(\boxed{b}\)[/tex].
