Find which two consecutive whole numbers the square root is between. Write the letter of the exercise on the number line between these two numbers.
[tex]\sqrt{30}[/tex], [tex]\sqrt{2}[/tex], [tex]\sqrt{45}[/tex], [tex]\sqrt{8}[/tex], [tex]\sqrt{23}[/tex], [tex]\sqrt{120}[/tex], [tex]\sqrt{138}[/tex], [tex]\sqrt{82}[/tex], [tex]\sqrt{11}[/tex], [tex]\sqrt{70}[/tex], [tex]\sqrt{0.5}[/tex], [tex]\sqrt{59}[/tex]
Answer (2)
\sqrt{30}\\\\5 < \sqrt{30} < 6\\-------------\\1=\sqrt{1^2}=\sqrt1 < \sqrt2\\2=\sqrt{2^2}=\sqrt4 > \sqrt2\\\\1 < \sqrt2 < 2\\-------------\\6=\sqrt{6^2}=\sqrt{36} < \sqrt{45}\\7=\sqrt{7^2}=\sqrt{49} > \sqrt{45}\\\\6 < \sqrt{45} < 7\\-------------"> 5 = 5 2 = 25 < 30 6 = 6 2 = 36 > 30 5 < 30 < 6 − − − − − − − − − − − − − 1 = 1 2 = 1 < 2 2 = 2 2 = 4 > 2 1 < 2 < 2 − − − − − − − − − − − − − 6 = 6 2 = 36 < 45 7 = 7 2 = 49 > 45 6 < 45 < 7 − − − − − − − − − − − − −
\sqrt8\\\\2 < \sqrt8 < 3\\-------------\\10=\sqrt{10^2}=\sqrt{100} < \sqrt{120}\\11=\sqrt{11^2}=\sqrt{121} > \sqrt{120}\\\\10 < \sqrt{120} < 11\\-------------\\12=\sqrt{12^2}=\sqrt{144} < \sqrt{138}\\13=\sqrt{13^2}=\sqrt{169} > \sqrt{138}\\\\12 < \sqrt{138} < 13\\-------------"> 2 = 2 2 = 4 < 8 3 = 3 2 = 9 > 8 2 < 8 < 3 − − − − − − − − − − − − − 10 = 1 0 2 = 100 < 120 11 = 1 1 2 = 121 > 120 10 < 120 < 11 − − − − − − − − − − − − − 12 = 1 2 2 = 144 < 138 13 = 1 3 2 = 169 > 138 12 < 138 < 13 − − − − − − − − − − − − −
\sqrt{82}\\\\9 < \sqrt{82} < 10\\-------------\\3=\sqrt{3^3}=\sqrt9 < \sqrt{11}\\4=\sqrt{4^2}=\sqrt{16} > \sqrt{11}\\\\3 < \sqrt{11} < 4\\-------------\\8=\sqrt{8^2}=\sqrt{64} < \sqrt{70}\\9=\sqrt{9^2}=\sqrt{81} > \sqrt{70}\\\\8 < \sqrt{70} < 9\\-------------"> 9 = 9 2 = 81 < 82 10 = 1 0 2 = 100 > 82 9 < 82 < 10 − − − − − − − − − − − − − 3 = 3 3 = 9 < 11 4 = 4 2 = 16 > 11 3 < 11 < 4 − − − − − − − − − − − − − 8 = 8 2 = 64 < 70 9 = 9 2 = 81 > 70 8 < 70 < 9 − − − − − − − − − − − − −
\sqrt{0.5}\\\\0 < \sqrt{0.5} < 1\\-------------\\7=\sqrt{7^2}=\sqrt{49} < \sqrt{59}\\8=\sqrt{8^2}=\sqrt{64} > \sqrt{59}\\\\7 < \sqrt{59} < 8"> 0 = 0 2 = 0 < 0.5 1 = 1 2 = 1 > 0.5 0 < 0.5 < 1 − − − − − − − − − − − − − 7 = 7 2 = 49 < 59 8 = 8 2 = 64 > 59 7 < 59 < 8
The square roots lie between the following consecutive whole numbers: 30 is between 5 and 6, 2 is between 1 and 2, 45 is between 6 and 7, 8 is between 2 and 3, and so on for the other values listed. Each square root approximation shows the range of values clearly defined. This yields an understanding of how square roots compare to whole numbers without using a calculator.
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