Area of Rectangle with square roots?

Question

Find the area of the rectangle shown in the figure below. Simplify your answer as much as possible

sqrt3 + sqrt5

(one side of rectangle)

sqrt3 + sqrt5

(other side of rectangle)

Answer 1

this is a square, but anyway try this

let the first side = x
so x = sqrt3 + sqrt5

let other side = y
so y = sqrt3 + sqrt5

area of rectangle
= x.y
= (sqrt3 + sqrt5).(sqrt3 + sqrt5) ***substitute values
= sqrt3.sqrt3 + 2.sqrt5.sqrt3 + sqrt5.sqrt5 ***distribute
= 3 + 2.sqrt5.sqrt3 + 5
= 8 + 2.sqrt5.sqrt3

then I'd have a look at what those values come out to be on the calculator :)

Answer 2

This is a rectangle, actually a square with dimensions:

(√3 + √5) by (√3 + √5)

The area of the rectangle is therefore:

(√3 + √5)(√3 + √5) = 3 + √(3*5) + √(5*3) + 5 = 8 + 2√15

Answer 3

Width = 3 root 5 length = 4 root 10 root 10 = root 2 cases root 5 as section is length cases width and substitution for root 10 section = thrice root 5 cases 4 cases root 5 cases root 2 as root 5 cases root 5 is 5 we get 3 x 5 x 4 x root 2 ie section is 60 root 2 sq. centimeters.

Answer 4

Multiply the two sides together, distribute one set through on the other then distribute the individual terms on the remaining set twice (once for each term) and then remove the radicals that you can and leave the others since they are in their most simplified form.

Answer 5

seeing that both sides of this object are equal, it is not a rectangle but it is a square. therefore it area is (sp rt3 + sq rt5) * (sq rt3 + sqrt5) = 15.75

Answer 6

8 + sqrt15

Answer 7

AREA OF RECTANGLE = A X B

ANSWER = ( SQRT 3 + SQRT 5 ) X (SQRT 3 +SQRT 5 )

Answer 8

[sqr(3) + sqr(5)]^2
[sqr(3)]^2 + 2sqr(3)sqr(5) + [sqr(5)]^2
3 + 2sqr(15) + 5
8 + 2sqr(15)