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Choose a valid substitution for a square-root estimate

Expand 1−x/(1+2x)\sqrt{1-x}/(1+2x) through x2x^2. marks

(i) A student substitutes x=−1x=-1 to estimate 2\sqrt2. Explain why this is wrong. mark

(ii) Put x=1/9x=1/9 in the expansion to show 2≈p/1296\sqrt2\approx p/1296, and find the positive integer pp. marks

[2001/RJC/I/16(a)]

CJC · Review problems · Question 3

After substituting 1/9, simplify the left-hand expression before solving for sqrt(2).

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