Question

How do you find the area of a rectangular object which has a length of 5 square root of 8 inches and a width of 2 square root of 5 inches?

Answer 1

`20sqrt10" square inches"`

Explanation:

The area ( A) of a rectangle is `color(red)(bar(ul(|color(white)(a/a)color(black)(A=lxxb)color(white)(a/a)|)))`
where l is the length and b, the width.

here `l=5sqrt8" and " b=2sqrt5`

`rArrA=5sqrt8xx2sqrt5`

`color(orange)"Reminder " color(red)(bar(ul(|color(white)(a/a)color(black)(sqrtaxxsqrtbhArrsqrt(ab))color(white)(a/a)|)))`

`rArrA=color(blue)(5)xxcolor(red)(sqrt8)xxcolor(blue)(2)xxcolor(red)(sqrt5)`

`=color(blue)(10)xxcolor(red)(sqrt40)`

Now `sqrt40=sqrt(4xx10)=sqrt4xxsqrt10=2xxsqrt10`

`rArrA=color(blue)(10)xxcolor(red)(sqrt40)=10xx2xxsqrt10`

`rArrA=20xxsqrt10=20sqrt10" square inches"`