# The area of a square is 121 square units. What is the length of its sides?

Apr 3, 2016

$11$

#### Explanation:

color(blue)(Area color(blue)(of color(blue)(a color(blue)(square $= s \cdot s = {s}^{2}$ $u n i t s$

Where $s$ is the side

$\rightarrow {s}^{2} = 121$

Take the square root of both sides

$\rightarrow \sqrt{{x}^{2}} = \sqrt{121}$

$\rightarrow x = \sqrt{121}$

color(green)(rArrx=11

Oct 20, 2016

$\sqrt{121} = 11$

#### Explanation:

Errors on this type of question are very common!

The most common mistakes are that people either

$\rightarrow$divide the area by 4, (supposedly because a square has 4 sides.)

$\rightarrow$ divide the area by 2, (knowing that the area is found using the length of 2 sides.

The correct operation is to find $\sqrt{121}$

Square roots are really not an easy concept to master at first, because of the irony that you can't find the answer until you know what the answer is!

Or put another way, you don't know what to divide by until you know the answer, and you can't find the answer until you know what to divide by!

It is a help to know all the square numbers up to ${20}^{2}$ by heart.
Recognition is half the battle!

$\sqrt{100} = 10$ is easy if you know that $10 \times 10 = 100$
$\sqrt{81} = 9$ is easy if you know that $9 \times 9 = 81$
$\sqrt{400} = 20$ is easy if you know that $20 \times 20 = 400$

Once you know the common ones by heart, it makes it easier to understanding others.

With a square root question - ask yourself...
"What number, multiplied by ITSELF will give this value?"

$\sqrt{121} = \sqrt{11 \times 11} = 11$