+73 1. The square root of a number has been graphed on the number line.
√?
<----------7----------8-------------9-----•---------10--------------11---------->
a. Which two numbers on the number line does the number lie between? What are those numbers squared?
b. Which squared number from part a will the number be closest to? How do you know?
c. Suppose the point on the number line is 9.33. What square root would be graphed on the number line (round to the nearest whole number)? Explain how you found your answer.
2. The square below has a side length of √5.
√5
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a. Is √5 a rational or irrational number?
b. Estimate the value of √5. Explain your reasoning.
c. What is the area of this square? Show your work and explain how you know.
+129852 1 (a) between 9 and 10 9^2 = 81 and 10^2 = 100
(b) it will lie closest to 81.......note....the number appears to be < 9.5......and 9.5^2 = 90.25 and 90.25 is closer to 81 than 100, so something between 9 and 9.5 squared will also lie closer to 81
(c) I'm assuming that the question refers to the square root of 9.33......the square root of this is a little larger than 3 since sqrt(9) = 3.........so 3 would be graphed on the number line if we were rounding the square root of 9.33 to the nearest whole number
2 (a) √5 is definitely irrational
(b) √5 will be a little larger than 2 since √4 = 2
(c) Area of a square = side^2....so ...... (√5)^2 = (√5) * (√5) = 5 squre units is the area
