SQRT

Returns the positive square root of a number.

Syntax:

SQRT(number)

Returns the positive square root of number. number must be positive.

Example:

SQRT(16)

returns 4.

SQRT(-16)

returns an invalid argument error.

Application:

An application of using the SQRT function is in calculating the length of the sides of a right-angled triangle. This is a common application in fields like construction, engineering, and navigation, where precise measurements are crucial.

Consider a scenario where a construction worker needs to determine the length of a diagonal brace for a rectangular frame to ensure it's perfectly square. The frame has a height of 4 meters and a width of 3 meters. The length of the diagonal brace can be found using the Pythagorean theorem, which states that for a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

The formula is:

$a^{2} + b^{2} = c^{2}$

Where:

a is the height of the frame (3 meters)
b is the width of the frame (4 meters)
c is the length of the diagonal brace

To find c, we need to take the square root of $a^{2} + b^{2}$ . This is where the SQRT function comes in.

The calculation would be:

Square the height: 32=9
Square the width: 42=16
Add the results: 9+16=25
Take the square root of the sum using the SQRT function: SQRT(25) = 5

So, the length of the diagonal brace should be 5 meters.

Here is a table summarizing the calculation for different frame dimensions:

	Height (a)	Width (b)	$a^{2}$	$b^{2}$	$a^{2} + b^{2}$	Diagonal (c) = SQRT( $a^{2} + b^{2}$ )
	A	B	C	D	E	F
1	3	4	9	16	25	5
2	5	12	25	144	169	13
3	8	15	64	225	289	17