# std::sqrt(std::valarray)

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< cpp‎ | numeric‎ | valarray

Defined in header `<valarray>` |  |
template< class T > valarray<T> sqrt( const valarray<T>& va ); |  |

For each element in `va` computes the square root of the value of the element.

### Parameters

va | - | value array to apply the operation to

### Return value

Value array containing square roots of the values in `va`.

### Notes

Unqualified function (sqrt) is used to perform the computation. If such function is not available, std::sqrt is used due to argument dependent lookup.

The function can be implemented with the return type different from std::valarray. In this case, the replacement type has the following properties:

  - All const member functions of std::valarray are provided.
  - std::valarray, std::slice_array, std::gslice_array, std::mask_array and std::indirect_array can be constructed from the replacement type.
  - All functions accepting an argument of type const std::valarray& except `begin()` and `end()` (since C++11) should also accept the replacement type.
  - All functions accepting two arguments of type const std::valarray& should accept every combination of const std::valarray& and the replacement type.
  - The return type does not add more than two levels of template nesting over the most deeply-nested argument type.

### Possible implementation

    template<class T>
    valarray<T> sqrt(const valarray<T>& va)
    {
        valarray<T> other = va;
        for (T &i : other) {
            i = sqrt(i);
        }
        return other;
    }

### Example

Finds real roots of multiple quadratic equations.

Run this code

    #include <valarray>
    #include <iostream>

    int main()
    {
        std::valarray<double> a(1, 8);
        std::valarray<double> b{1, 2, 3, 4, 5, 6, 7, 8};
        std::valarray<double> c = -b;
        // literals must also be of type T (double in this case)
        std::valarray<double> d = std::sqrt((b * b - 4.0 * a * c));
        std::valarray<double> x1 = (-b - d) / (2.0 * a);
        std::valarray<double> x2 = (-b + d) / (2.0 * a);
        std::cout << "quadratic equation    root 1,  root 2" << "\n";
        for (size_t i = 0; i < a.size(); ++i) {
            std::cout << a[i] << "x\u00B2 + " << b[i] << "x + " << c[i] << " = 0   ";
            std::cout << x1[i] << ", " << x2[i] << "\n";
        }
    }

Output:

    quadratic equation    root 1,  root 2
    1x² + 1x + -1 = 0   -1.61803, 0.618034
    1x² + 2x + -2 = 0   -2.73205, 0.732051
    1x² + 3x + -3 = 0   -3.79129, 0.791288
    1x² + 4x + -4 = 0   -4.82843, 0.828427
    1x² + 5x + -5 = 0   -5.8541, 0.854102
    1x² + 6x + -6 = 0   -6.87298, 0.872983
    1x² + 7x + -7 = 0   -7.88748, 0.887482
    1x² + 8x + -8 = 0   -8.89898, 0.898979

### See also

pow(std::valarray) | applies the function std::pow to two valarrays or a valarray and a value (function template)
sqrt sqrtf sqrtl (C++11)(C++11) | computes square root (√x) (function)
sqrt(std::complex) | complex square root in the range of the right half-plane (function template)

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