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91.

y²= 9

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92.

straight z squared equals 0.04

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93. In the following equations, find which variables x, y, z etc., represent rational numbers and which represent irrational numbers:

straight u squared equals 17 over 4

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94.

straight v squared equals 3

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95. In the following equations, find which variables x, y, z etc., represent rational numbers and which represent irrational numbers:

straight w cubed equals 27

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96. In the following equations, find which variables x, y, z etc., represent rational numbers and which represent irrational numbers:

straight t squared equals 0.4

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97. Rationalise the denominators of the following:

fraction numerator square root of 3 minus 1 over denominator square root of 3 plus 1 end fraction

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98. Rationalise the denominators of the following:

fraction numerator 3 plus square root of 2 over denominator 3 minus square root of 2 end fraction

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fraction numerator 3 plus square root of 7 over denominator 3 minus 4 square root of 7 end fraction fraction numerator 3 plus square root of 7 over denominator 3 minus 4 square root of 7 end fraction equals fraction numerator 3 plus square root of 7 over denominator 3 minus 4 square root of 7 end fraction cross times fraction numerator 3 plus square root of 7 over denominator 3 plus 4 square root of 7 end fraction

Multliplying the numerator and denominator by

3 plus 4 square root of 7

equals fraction numerator left parenthesis 3 plus square root of 7 right parenthesis left parenthesis 3 plus 4 square root of 7 right parenthesis over denominator left parenthesis 3 right parenthesis squared minus left parenthesis 4 square root of 7 right parenthesis squared end fraction equals fraction numerator 3 left parenthesis 3 plus 4 square root of 7 right parenthesis plus square root of 7 left parenthesis 3 plus 4 square root of 7 right parenthesis over denominator 9 minus 112 end fraction equals space fraction numerator 9 plus 12 square root of 7 plus 3 square root of 7 plus 28 over denominator negative 103 end fraction equals fraction numerator 37 plus 15 square root of 7 over denominator negative 103 end fraction equals negative fraction numerator 37 plus 15 square root of 7 over denominator 103 end fraction

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100. Represent

square root of 5

on the number line.

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