Chapter 8.1, Problem 18MC

MATHEMATICAL CONNECTIONS

A student wants to know what is wrong with the following “proof” that $1=1.$ How do you respond?

$\sqrt{a}\sqrt{b}=\sqrt{ab}$

Let $a=b=1.$

$\sqrt{1}\sqrt{1}=\sqrt{\left(1\right)\left(1\right)}=\sqrt{1}=1$

Butalso $\sqrt{1}\sqrt{1}=1.$

Thus, $1=1.$