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Number Systems

Short Answer Type

111. Simplify:

12 square root of 18 minus 6 square root of 20 minus 3 square root of 50 plus 8 square root of 45

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112. If

straight x equals 3 plus 2 square root of 2 comma space find space square root of straight x plus fraction numerator 1 over denominator square root of straight x end fraction

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113. Simplify:

square root of 2 left parenthesis square root of 6 minus square root of 8 right parenthesis plus square root of 3 left parenthesis square root of 27 minus square root of 6 right parenthesis

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114. Simplify:

fraction numerator 1 plus square root of 2 over denominator square root of 5 plus square root of 3 end fraction plus fraction numerator 1 minus square root of 2 over denominator square root of 5 minus square root of 3 end fraction

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115. Find the simplified value of $fraction numerator 1 over denominator 5 minus 2 square root of 3 end fraction plus fraction numerator 1 over denominator 5 plus 2 square root of 3 end fraction$

Sollution not provided.

Ans. $10 over 13$

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116. If

straight x equals 3 minus 2 square root of 2

then find the value of

space space open parentheses straight x squared minus 1 over straight x squared close parentheses

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117.

If $straight x equals fraction numerator square root of 3 plus square root of 2 over denominator square root of 3 minus square root of 2 end fraction comma space space straight y space equals fraction numerator square root of 3 minus square root of 2 over denominator square root of 3 plus square root of 2 end fraction$ , then find the value of x² + y² - 10xy.

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118.

If $square root of 5 equals 2.236 space a n d space square root of 10 equals 3.162 comma$ find the value of $open parentheses fraction numerator square root of 10 minus square root of 5 over denominator square root of 2 end fraction close parentheses.$