chapter iv. concerning squares and roots equal to numbers: the following is an example of squares and roots equal to numbers: a square and 10 roots are equal to 39 units. so the question in this example can be stated as follows: what is the square which combined with ten of its roots will give a sum total of 39? the manner of solving this type of equation is to take one-half of the roots just mentioned. now the roots in the problem before us are 10. therefore take 5, which multiplied by itself gives 25, an amount which you add to 39, (giving 64). having taken then the square root of this, which is 8, subtract from it the half of the roots, 5, leaving 3. the number three therefore represents one root of this square, which itself, of course, is 9. nine therefore gives that square.