Clare was adding [math]\sqrt{4}[/math] and [math]\sqrt{9}[/math], and at first she wrote [math]\sqrt{4}+\sqrt{9}=2+3[/math]. But then she remembered that 2 and -2 both square to make 4, and that 3 and -3 both square to make 9. She wrote down all the possible combinations:[br]2 + 3 = 5[br]2 + (-3) = -1[br](-2) + 3 = 1[br](-2) + (-3) = -5[br][br]Then she wondered, “Which of these are the same as [math]\sqrt{4}+\sqrt{9}[/math]? All of them? Or only some? Or just one?”[br][br]How would you answer Clare’s question? Give reasons that support your answer.
[math]y^3=\text{-}1[/math]
[math]w^4=\text{-}81[/math]
[size=150]Write a rule to determine how many solutions there are to the equation [math]x^n=m[/math] where [math]n[/math] and [math]m[/math] are non-zero integers.[br][/size]
[size=150]The graph of [math]b=\sqrt{a}[/math] is shown.[/size]
Label the point on the graph above that shows the solution to [math]\sqrt{a}=4[/math].
Label the point on the graph above that shows the solution to [math]\sqrt{a}=5[/math].[br]
Label the point on the graph above that shows the solution to [math]\sqrt{a}=\sqrt{5}[/math].[br]
Label the point(s) on the graph that show(s) the solution(s) to [math]s^2=25[/math].[br]
Label the point(s) on the graph that show(s) the solution(s) to [math]\sqrt{t}=5[/math].[br]
Label the point(s) on the graph that show(s) the solution(s) to [math]s^2=5[/math].