Question

what is the following product? assume ( b geq 0 ).( sqrt{b} cdot sqrt{b} )options: ( bsqrt{b} ), ( 2sqrt{b} ), ( b^2 ), ( b )

Explanation:

Step1: Recall the property of square roots

For non - negative real numbers \(a\) and \(b\), \(\sqrt{a}\cdot\sqrt{b}=\sqrt{ab}\). Here we have \(\sqrt{b}\cdot\sqrt{b}\), so by this property, \(\sqrt{b}\cdot\sqrt{b}=\sqrt{b\times b}\).

Step2: Simplify the square root

Since \(b\times b = b^{2}\) and \(b\geq0\), \(\sqrt{b^{2}}=b\) (because for \(x\geq0\), \(\sqrt{x^{2}} = x\)).

Answer:

\(b\) (the last option among the given choices, the one with the label \(b\))