Answer:
See below ~
Step-by-step explanation:
Analyzing Question 2 :
⇒ [tex]\sqrt{\frac{15}{2} }[/tex]
⇒ [tex]\frac{\sqrt{15} }{\sqrt{2} }[/tex] (Correct)
⇒ [tex]\frac{\sqrt{15} }{\sqrt{2} } \times \frac{\sqrt{2} }{\sqrt{2} }[/tex] (Correct)
⇒ [tex]\frac{\sqrt{30} }{\sqrt{2}}[/tex] (Incorrect ×)
This step is incorrect because on multiplying the denominator it should be √4, equal to 2.
The correct step will be :
⇒ [tex]\frac{\sqrt{30} }{2}[/tex] (Correct) (Final solution)
Analyzing Question 3 :
⇒ [tex]x^{2} - 4 = 0[/tex]
⇒ [tex]\sqrt{x^{2} -4} = 0[/tex] (Step is theoretically correct, but solution won't be possible here)
⇒ [tex]x-2=0[/tex] (Incorrect ×)
This step is incorrect because the square root of x² - 4 cannot be taken. (x - 2) would be the value of the root of (x - 2)² = x² - 4x + 4.
Resolving by alternative method :
⇒ [tex]x^{2} = 4[/tex] (Correct)
⇒ [tex]\sqrt{x^{2} } = \sqrt{4}[/tex] (Correct)
⇒ x = ±2 (Correct) (Final solution)
