Question

Consider the following statements
$S_1=-6=2i\times 3i=\sqrt{(-4)}\times \sqrt{(-9)}(where,i=\sqrt{-1})$
$S_2=\sqrt{(-4)}\times \sqrt{(-9)}=\sqrt{(-4)\times (-9)}$
$S_3:\sqrt{(-4)\times (-9)}=\sqrt{36}$
$S_4:\sqrt{36}=6$
of these statements, the incorrect one is

• A. $S_{1}only$
• B. $S_{2}only$
• C. $S_{3}only$
• D. $S_4$ only

Answer 1

Answer: (B)

$S_{2}only$

$S_1=\sqrt{-4}\times \sqrt{-9}$

$=\sqrt{-1}\times \sqrt{4}\times \sqrt{-1}\times \sqrt{9}$

$=\sqrt{-1}\times 2\times i\times 3$

$=2i\times 3i$

$=6i^2=-6$ is true

$S_2=\sqrt{(-4)\times (-9)}$

$=\sqrt{36}=\sqrt{4\times 9}\ne \sqrt{4}\times \sqrt{9}\ne \sqrt{-4}\times \sqrt{-9}$ since $\sqrt{-4}\times \sqrt{-9}=2i\times 3i=6i^2=-6$

Hence $S_2$ is not true.

$S_3=\sqrt{(-4)\times (-9)}=\sqrt{36}$ is true.

$S_4=\sqrt{36}=\sqrt{6\times 6}=6$ is true