what is the following product? assume ( bgeq0 ).\n( sqrt{b}cdotsqrt{b} )\n( bsqrt{b} )\n( 2sqrt{b} )\n( b…

what is the following product? assume ( bgeq0 ).\n( sqrt{b}cdotsqrt{b} )\n( bsqrt{b} )\n( 2sqrt{b} )\n( b )\n( b^{2} )

what is the following product? assume ( bgeq0 ).\n( sqrt{b}cdotsqrt{b} )\n( bsqrt{b} )\n( 2sqrt{b} )\n( b )\n( b^{2} )

Answer

Explanation:

Step1: Use the property of square - root multiplication

The property of square - root multiplication is (\sqrt{a}\cdot\sqrt{b}=\sqrt{ab}) (when (a\geq0) and (b\geq0)). For (\sqrt{b}\cdot\sqrt{b}), we have (\sqrt{b}\cdot\sqrt{b}=\sqrt{b\times b}).

Step2: Simplify the expression

Since (b\times b = b^{2}), then (\sqrt{b\times b}=\sqrt{b^{2}}). And for (b\geq0), (\sqrt{b^{2}}=b).

Answer:

C. (b)