Certainly! Let's break down the given problem step-by-step.
We need to compute the product of [tex]\(\sqrt{b}\)[/tex] and [tex]\(\sqrt{b}\)[/tex], where [tex]\(b \geq 0\)[/tex].
### Step-by-Step Solution:
1. Express the problem in mathematical notation:
[tex]\[
\sqrt{b} \cdot \sqrt{b}
\][/tex]
2. Recall the property of square roots:
The square root of a product is the product of the square roots. That is, if [tex]\( a \geq 0 \)[/tex] and [tex]\( b \geq 0 \)[/tex], then:
[tex]\[
\sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b}
\][/tex]
3. Apply this property to our expression:
Here, we have [tex]\(a = b\)[/tex] and [tex]\(b = b\)[/tex]:
[tex]\[
\sqrt{b} \cdot \sqrt{b} = \sqrt{b \cdot b}
\][/tex]
4. Simplify the product inside the square root:
[tex]\[
b \cdot b = b^2
\][/tex]
5. Take the square root of the resulting expression:
[tex]\[
\sqrt{b^2}
\][/tex]
6. Using the property of square roots, [tex]\(\sqrt{b^2} = b\)[/tex] for [tex]\(b \geq 0\)[/tex], we can simplify:
[tex]\[
\sqrt{b^2} = b
\][/tex]
Therefore, the product [tex]\(\sqrt{b} \cdot \sqrt{b}\)[/tex] simplifies to [tex]\(b\)[/tex].
### Conclusion:
[tex]\[
\sqrt{b} \cdot \sqrt{b} = b
\][/tex]
So, the answer to the given question is [tex]\(b\)[/tex].
