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SQRT

Returns the square root of a number.

Quick Example​

=SQRT(16)

Returns 4.

Syntax​

=SQRT(number)

Arguments​

  • number (required): The number for which you want the square root. Must be non-negative (≥ 0).

Examples​

Basic Square Root​

=SQRT(25)

Returns 5

Perfect Square​

=SQRT(100)

Returns 10

Non-Perfect Square​

=SQRT(50)

Returns 7.071067811865476 (approximately 7.07)

Square Root of 2​

=SQRT(2)

Returns 1.4142135623730951

Zero​

=SQRT(0)

Returns 0

Cell Reference​

=SQRT(A1)

If A1 = 144, returns 12

How It Works​

Mathematical Definition​

The square root of a number n is the value that, when multiplied by itself, equals n:

  • SQRT(16) = 4 because 4 × 4 = 16
  • SQRT(2) ≈ 1.414 because 1.414 × 1.414 ≈ 2

Non-Negative Requirement​

The number must be ≥ 0. Negative numbers return an error:

=SQRT(-4)

Returns #NUM! error (cannot take square root of negative number)

Single Cell References​

If you pass a range that refers to a single cell, SQRT extracts the value:

=SQRT(A1)

Gets the value in A1 and returns its square root

Multi-Cell Ranges Not Supported​

=SQRT(A1:A10)

Returns #VALUE! error (SQRT only works with single values)

Common Use Cases​

Calculate Standard Deviation Components​

=SQRT(SUM((A1:A10-AVERAGE(A1:A10))^2)/COUNT(A1:A10))

Part of standard deviation calculation

Distance Formula​

=SQRT((X2-X1)^2 + (Y2-Y1)^2)

Calculate distance between two points

Pythagorean Theorem​

=SQRT(A1^2 + B1^2)

Find the hypotenuse of a right triangle

Root Mean Square​

=SQRT(AVERAGE(A1:A10^2))

Calculate RMS of a set of values

Normalize Values​

=A1/SQRT(SUM(A1:A10^2))

Normalize a value

Error Handling​

Negative Number Error​

If the argument is negative, SQRT returns #NUM!:

=SQRT(-16)

Returns #NUM! error

Error Propagation​

If the argument contains an error, SQRT returns that error:

=SQRT(#DIV/0!)

Returns #DIV/0!

Common Errors​

ErrorCauseSolution
#NUM!Negative numberEnsure the number is ≥ 0
#VALUE!Non-numeric argument or multi-cell rangeEnsure argument is a single number or cell reference
#REF!Invalid cell referenceVerify cell reference exists
#NAME?Function name misspelledCheck spelling: =SQRT not =SQR

Technical Details​

Implementation Notes​

  • Requires exactly 1 argument
  • Only accepts single values or single-cell references
  • Uses standard square root function from C++ std::sqrt()
  • Returns floating-point result with full precision
  • Does not work with multi-cell ranges

Type Coercion​

Text that can be converted to numbers is accepted:

=SQRT("64")

Returns 8 (string is coerced to number)

Precision​

SQRT returns results with full floating-point precision:

=SQRT(2)

Returns 1.4142135623730951 (15+ decimal places)

Mathematical Properties​

Inverse of Squaring​

SQRT is the inverse operation of squaring:

=SQRT(5^2)  // Returns 5
=(SQRT(5))^2  // Returns 5

Square Root of Product​

=SQRT(A1*B1) = SQRT(A1) * SQRT(B1)

The square root of a product equals the product of the square roots

Advanced Examples​

Ensure Non-Negative Input​

=SQRT(ABS(A1))

Use ABS to ensure the value is non-negative

Conditional Square Root​

=IF(A1>=0, SQRT(A1), "Invalid")

Check if value is non-negative before calculating

Geometric Mean​

=SQRT(A1*B1)

Calculate geometric mean of two numbers

  • ABS - Absolute value
  • ROUND - Round numbers
  • PI - Pi constant
  • SUM - Add numbers