help pre calculus

Question

A square has an area of 98 m². What is the perimeter of the square as a mixed radical. Show work :)

Answer 1

Actual Area of the square A = 98 m²

Let side of the square = x

Perimeter of the square P = 4x

Area of the square = x²

Area of the square = Actual Area of the square

x² = 98

x = √98

Perimeter of the square P = 4x

P = 4√98 m

Converting 4√98 in simplified radical :

P = 4√98

98 = 2*49

= 2*7²

= 4√(2*7²)

Use formula : √(ab) = √(a)√(b)

= 4√(2)√(7²)

Use formula : √(a²) = a

= 4(√2)(7)

= (7*4)√2

= 28√2

Perimeter of the square as a mixed radical is 28√2 m.