Answer:
Statement (i) , (ii) are TRUE and
The statement (iii) is FALSE.
Step-by-step explanation:
Given : a , b are strictly greater than 0.
Now, let us take each statements.
(i) 2(a +b) = 2a + 2b
Yes, the given statement is TRUE, as by DISTRIBUTIVE PROPERTY we get that x (y + z) = xy + xz
(ii)[tex]\frac{a + b}{2} = \frac{a}{2} + \frac{b}{2}[/tex]
Yes, the given statement is TRUE, as by DISTRIBUTIVE PROPERTY we get that [tex]\frac{m + n}{k} = \frac{m}{k} + \frac{n}{k}[/tex]
(iii[tex]\sqrt{(a +b)} = \sqrt{a} + \sqrt{b}[/tex]
Here, the given statement is FALSE.
Because, if we have a = 2 and b = 3, then
[tex]\sqrt{(2+ 3} ) = \sqrt{5} = 2.23\\\sqrt{2} + \sqrt{3} = 1.41 + 1.73 = 3.14\\[/tex]
and 2.23 ≠ 3.24
So,[tex]\sqrt{(a +b)} \neq \sqrt{a} + \sqrt{b}[/tex]
