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Number Systems

Short Answer Type

101. Represent $square root of 4.7 end root$ on the number line.

Mark the distance 4.7 units from a fixed point A on a given line to obtain a point B such that AB = 4.7 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 semicircle with centre O and radius OC. Draw a line perpendicular to AC passing through B and intersecting the semicircle at D. Then,

BD space equals space square root of 4.7 end root.

Now, let us treat the line BC as the number line, with B as zero, C as 1, and so on. Draw an arc with centre B and radius BD, which intersects the number line in E.

Then, E represents $square root of 4.7 end root.$

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102. Check whether

7 square root of 5 comma fraction numerator 7 over denominator square root of 5 comma end fraction comma space square root of 2 plus 21 comma space space straight pi minus 5

are irrational numbers or not.

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103. Add

2 square root of 2 plus 5 square root of 3 space and space square root of 2 minus 3 square root of 3.

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104. Multiply

6 square root of 5 space by space 2 square root of 5.

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105. Divide

8 square root of 15 space by space 2 square root of 5.

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106. Rationalise the denominator of

fraction numerator 1 over denominator square root of 2 end fraction.

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107. Rationalise the denominator of

fraction numerator 5 over denominator square root of 3 minus square root of 5 end fraction.

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108.

If $fraction numerator square root of 3 minus 1 over denominator square root of 3 plus 1 end fraction equals space straight a plus straight b square root of 3$ find the values of a and b.