randFromArray([2, 3, 5, 6, 7, 10, 11, 13])
randRangeUnique( 1, 5, 2 ) pow( A_COEFF, 2 ) * NUM pow( B_COEFF, 2 ) * NUM

Simplify the following expression:

\sqrt{A} + \sqrt{B}

pow( A_COEFF + B_COEFF, 2 ) * NUM

First, try to factor any perfect squares out of the radicals.

= \sqrt{A} + \sqrt{B}

= \sqrt{pow( A_COEFF, 2 ) \cdot NUM} + \sqrt{pow( B_COEFF, 2 ) \cdot NUM}

= \sqrt{pow( A_COEFF, 2 )} \cdot \sqrt{NUM} + \sqrt{pow( B_COEFF, 2 )} \cdot \sqrt{NUM}

= A_COEFF\sqrt{NUM} + B_COEFF\sqrt{NUM}

Finally, simplify by combining the terms.

= ( A_COEFF + B_COEFF )\sqrt{NUM} = A_COEFF + B_COEFF\sqrt{NUM}

randRange( 2, 5 ) randRange( 1, A_COEFF - 1 ) pow( A_COEFF, 2 ) * NUM pow( B_COEFF, 2 ) * NUM

Simplify the following expression:

\sqrt{A} - \sqrt{B}

pow( A_COEFF - B_COEFF, 2 ) * NUM

First, try to factor any perfect squares out of the radicals.

= \sqrt{A} - \sqrt{B}

= \sqrt{pow( A_COEFF, 2 ) \cdot NUM} - \sqrt{pow( B_COEFF, 2 ) \cdot NUM}

= \sqrt{pow( A_COEFF, 2 )} \cdot \sqrt{NUM} - \sqrt{pow( B_COEFF, 2 )} \cdot \sqrt{NUM}

= A_COEFF\sqrt{NUM} - B_COEFF\sqrt{NUM}

Finally, simplify by combining the terms.

= ( A_COEFF - B_COEFF )\sqrt{NUM} = A_COEFF - B_COEFF\sqrt{NUM}

(function() { var coeffs = [1, 2, 3, 4, 5]; var shuffled = shuffle( coeffs, 3 ); shuffled[1] *= randRangeNonZero( -1, 1 ); shuffled[2] *= randRangeNonZero( -1, 1 ); while ( shuffled[0] + shuffled[1] + shuffled[2] <= 0 ) { shuffled[1] *= randRangeNonZero( -1, 1 ); shuffled[2] *= randRangeNonZero( -1, 1 ); } return shuffled; })() COEFFS[0] COEFFS[1] COEFFS[2] pow( A_COEFF, 2 ) * NUM pow( B_COEFF, 2 ) * NUM pow( C_COEFF, 2 ) * NUM B_COEFF > 0 ? "+" : "-" C_COEFF > 0 ? "+" : "-"

Simplify the following expression:

\sqrt{A}B_SIGN\sqrt{B}C_SIGN\sqrt{C}

pow( A_COEFF + B_COEFF + C_COEFF, 2 ) * NUM

First, try to factor any perfect squares out of the radicals.

= \sqrt{A}B_SIGN\sqrt{B}C_SIGN\sqrt{C}

= \sqrt{pow( A_COEFF, 2 ) \cdot NUM}B_SIGN\sqrt{pow( B_COEFF, 2 ) \cdot NUM}C_SIGN\sqrt{pow( C_COEFF, 2 ) \cdot NUM}

= \sqrt{pow( A_COEFF, 2 )} \cdot \sqrt{NUM}B_SIGN\sqrt{pow( B_COEFF, 2 )} \cdot \sqrt{NUM}C_SIGN\sqrt{pow( C_COEFF, 2 )} \cdot \sqrt{NUM}
= A_COEFF\sqrt{NUM}B_SIGNabs( B_COEFF )\sqrt{NUM}C_SIGNabs( C_COEFF )\sqrt{NUM}
= ( A_COEFF + B_COEFF + C_COEFF )\sqrt{NUM} = A_COEFF + B_COEFF + C_COEFF\sqrt{NUM} = 0