Rationalise the denominators of the following: from Mathematics

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 Multiple Choice QuestionsShort Answer Type

91.

y= 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


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

Multiplying the numerator and denominator by square root of 3 minus 1

equals fraction numerator left parenthesis square root of 3 minus 1 right parenthesis squared over denominator open parentheses square root of 3 close parentheses squared minus left parenthesis 1 right parenthesis squared end fraction equals fraction numerator left parenthesis square root of 3 right parenthesis squared minus 2 left parenthesis square root of 3 right parenthesis left parenthesis 1 right parenthesis plus left parenthesis 1 right parenthesis squared over denominator 3 minus 1 end fraction
equals space fraction numerator 3 minus 2 square root of 3 plus 1 over denominator 2 end fraction equals fraction numerator 4 minus 2 square root of 3 over denominator 2 end fraction equals 2 minus square root of 3.
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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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99. Rationalise the denominators of the following:

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

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100. Represent square root of 5on the number line.
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