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Simplify radicals in arithmetical expressions

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radsimp(z) tries to simplify the radicals in the expression z. The result is mathematically equivalent to z.

radsimp and simplifyRadical are equivalent.


Example 1

Simplify these constant expressions with square roots and higher order radicals:

radsimp(3*sqrt(7)/(sqrt(7) - 2)),
radsimp(sqrt(5 + 2*sqrt(6)));
radsimp(sqrt(5*sqrt(3) + 6*sqrt(2))),
radsimp(sqrt(3 + 2*sqrt(2)))

radsimp((1/2 + 1/4*3^(1/2))^(1/2))

radsimp((5^(1/3) - 4^(1/3))^(1/2))

radsimp(sqrt(3*sqrt(3 + 2*sqrt(5 - 12*sqrt(3 - 2*sqrt(2))))
             + 14))

radsimp(2*2^(1/4) + 2^(3/4) - (6*2^(1/2) + 8)^(1/2))

radsimp(sqrt(1 + sqrt(3)) + sqrt(3 + 3*sqrt(3))
             - sqrt(10 + 6*sqrt(3)))

Example 2

Create the following expression and then simplify it using radsimp:

x := sqrt(3)*I/2 + 1/2: y := x^(1/3) + x^(-1/3): z := y^3 - 3*y


delete x, y, z:

Example 3

Use radsimp to simplify these arithmetical expressions containing variables:

z := x/(sqrt(3) - 1) - x/2

radsimp(z) = expand(radsimp(z))

delete z:

Example 4

Use radsimp to simplify nested radicals. When simplifying nested radicals, radsimp tries to reduce the nesting depth:

radsimp((6*2^(1/2) + 8)^(1/2));
radsimp(((32/5)^(1/5) - (27/5)^(1/5))^(1/3));
radsimp(sqrt((3+2^(1/3))^(1/2) * (4-2^(1/3))^(1/2)))



An arithmetical expression

Return Values

Arithmetical expression.


Borodin A., Fagin R., Hopcroft J.E., and Tompa M.: Decreasing the Nesting Depth of Expressions Involving Square Roots, JSC 1, 1985, pp. 169-188.

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