square root problem

[davellew69]

hi all, can someone explain why 1/2 a^2 =a/sqroot 2

cheers

dave

 

[wjm11]

hi all, can someone explain why 1/2 a^2 =a/sqroot 2

The equation has only one solution for "a". Is that what you are supposed to find? To find "a", multiply both sides of the equation by 2, then divide both sides by "a".

Also, it is a good idea to use grouping symbols (parentheses) for clarity when multiplying, especially when using fractions: 1/2 a^2 = (1/2)(a^2).

 

[Deleted member 4993]

hi all, can someone explain why 1/2 a^2 =a/sqroot 2

cheers

dave

I am assuming you want to see the steps to get the following:

\(\displaystyle \displaystyle \sqrt{\left [\dfrac{1}{2}a^2 \right ]} \ = \ \dfrac{a}{\sqrt{2}} \)

Here are the steps:

\(\displaystyle \displaystyle \sqrt{\left [\dfrac{a^2}{2} \right ]} \ = \ \dfrac{\sqrt{a^2}}{\sqrt{2}}\ = \ \dfrac{a}{\sqrt{2}}\)

 

[lookagain]

hi all, can someone explain why 1/2 a^2 =a/sqroot 2

cheers

dave

dave,

if you are, in fact, in beginning algebra, then it is likely that the variable, a, is assumed to be non-negative. With that restriction,

\(\displaystyle \sqrt{a^2} = a.\)