Answer: [tex]12*\sqrt{2}[/tex]
Step-by-step explanation:
We have the equation:
[tex]\frac{14}{\sqrt{2} } + \sqrt{50}[/tex]
we know that:
14*14 = 196
then:
14 = √196
[tex]\frac{\sqrt{196} }{\sqrt{2} } + \sqrt{50} = \sqrt{196/2} + \sqrt{50} = \sqrt{98} + \sqrt{50}[/tex]
Now, we can rewrite:
50 = 2*25
98 = 2*49
This is because we know that 49 and 25 are perfect squares, then:
[tex]\sqrt{98} + \sqrt{50} = \sqrt{2*49} +\sqrt{2*25} = \sqrt{2} *\sqrt{49} + \sqrt{2} *\sqrt{25}[/tex]
Now we can use the common factor √2 and get:
[tex]\sqrt{2} *\sqrt{49} + \sqrt{2} *\sqrt{25} = \sqrt{2}*(\sqrt{49} + \sqrt{25} )[/tex]
and we know that:
7*7 = 49
5*5 = 25
then:
[tex]\sqrt{2}*(\sqrt{49} + \sqrt{25} ) = \sqrt{2}*(7 + 5) = 12*\sqrt{2}[/tex]
the value of b is:
b = 12
