Please help me answer the following questions on surds.

Question

1) Can a negative be a perfect square?

2) Is -67 an integer?

3) Is 3/7 an integer?

4) What is the square root of 729 with a little 3 on the left of the square root sign?

5) What is the square root of 29 with a little 3 on the left of the square root sign?

 

Thanks so much

Answer 1

1) no, because a negative is (-)(+) or (+)(-) and a perfect square is the square of an integer, not the square of an integer and its opposite; (-)(-)=+ and (+)(+)=+

2) yes, integers are the whole numbers and their opposites; ...-3,-2,-1,0,1,2,3,...

3) no, its a fraction

4) you mean cube root, not square root; 729=9*9*9 so the cube root of 729 is 9; you want x where x^3=729

5) do you mean cube root of 27 ? if so 3*3*3=27 and the cube root of 27 is 3; x^3=27, x=3

 if you mean cube root of 29, then use a calculator to get the approximation 3.07231682569...