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Number Systems

Short Answer Type

71. Classify the following numbers as rational or irrational:

fraction numerator 2 square root of 7 over denominator 7 square root of 7 end fraction

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72. Classify the following numbers as rational or irrational:

fraction numerator 1 over denominator square root of 2 end fraction

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73. Classify the following numbers as rational or irrational:

2 straight pi

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74. Simplify each of the following expressions:

left parenthesis 3 plus square root of 3 right parenthesis space left parenthesis 2 plus square root of 2 right parenthesis

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75. Simplify each of the following expressions:

left parenthesis 3 plus square root of 3 right parenthesis left parenthesis 3 minus square root of 3 right parenthesis

112 Views

76. Simplify each of the following expressions:

left parenthesis square root of 5 plus square root of 2 right parenthesis squared

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77. Simplify each of the following expressions:

left parenthesis space square root of 5 minus square root of 2 right parenthesis space left parenthesis square root of 5 plus square root of 2 right parenthesis

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78. Recall, π is defined as the ratio of the circumference (say c) of a circle to its diameter (say d). That is,

straight pi equals straight c over straight d

This seems to contradict the fact that π is irrational. How will you resolve this contradiction?

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79. Represent $square root of 9.3 end root$ on the number line.

Mark the distance 9.3 from a fixed point A on a given line to obtain a point B such that AB = 9.3 units. From B mark a distance of 1 unit and mark the new point as C. Find the mid-point of AC and mark that point as O. Draw a semi-circle with centre O and radius OC. Draw a line perpendicular to AC passing through B and intersecting the semi-circle at D. Then