Question

A square has an area of 49a^16 cm sq ? write an for the length of each side

Answer 1

7
`a^(8)`

Explanation:

the area (A) of a square is calculated as

A = s² ( s is the side length )

here A = 49
`a^(16)` , then

s² = 49
`a^(16)` ( take square root of both sides )

s =
`\sqrt{49a^(16) }` =
`√(49)` ×
`\sqrt{a^(16) }` = 7
`a^(8)`

Answer 2

Length of each side is
`\displaystyle{7a^8}`.

Explanation:

Area of Square

`\displaystyle{A = s^2}`

where A stands for area and s stands for side.

Given that a square has area of
`\displaystyle{49a^(16) \ \sf{cm^2}}`. We can substitute
`\displaystyle{A = 49a^(16)}` in the area equation:

`\displaystyle{49a^(16) = s^2}`

Solve the equation for s; square root both sides:

`\displaystyle{\sqrt{49a^(16)} = √(s^2)}\\\\\displaystyle{\sqrt{49a^(16)} = s}\\\\\displaystyle{\sqrt{7^2\left(a^(8)\right)^2} = s}\\\\\\\displaystyle{√(\left(7a^8\right)^2) = s}\\\\\displaystyle{7a^8 = s}`

Therefore, length of each side is
`\displaystyle{7a^8}`.