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Exercises under SQL Server is now checking on 2017 version.
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## POWER and SQRT functions

S.I.Moiseenko

The SQL Server POWER (x, y) function raises x to the power of y.
x is an expression of type FLOAT or of a type that can be implicitly converted to FLOAT.
y is an expression of a numeric type.

The returned result has the same type as x.

The returned result is of FLOAT type.

SQRT is the inverse function of POWER(x, 2), so that SQRT(POWER(x,2)) should return x.

Let’s check this

```select 3 x, power(3,2) y, sqrt(power(3,2)) sqrt_y;

x	y	sqrt_y
3	9	3
```

This is correct. However,

```select 3.1 x, power(3.1,2) y, sqrt(power(3.1,2)) sqrt_y;
```

yields

```x	y	sqrt_y
3.1	9.6	3,09838667696593
```

This unexpected result in most likelihood has to do with a loss of precision when the POWER function result type (which matches the type of the argument, NUMERIC) is implicitly converted to FLOAT.

Indeed,

```select SQL_VARIANT_PROPERTY(3.1,'BASETYPE') basetype;

basetype
numeric
```

When we apply an equivalent conversion to retain the NUMERIC type for the result

```select 3.1 x, power(3.1,2) y, power(power(3.1,2),0.5) sqrt_y;
```

everything works as expected.

```x	y	sqrt_y
3.1	9.6	3.1
```

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