NO CALCULATOR: if x is equal to an unknown number. The square root of y is equal to 2x. Given that z is equal to 1386 and z = 14y, what is x....

Friday, September 3, 2010

NO CALCULATOR: if x is equal to an unknown number. The square root of y is equal to 2x. Given that z is equal to 1386 and z = 14y, what is x....

x represents an unknown number. $\displaystyle\sqrt{{{y}}}={2}{x}$ . z=14y and z=1386. We are asked to determine x to three significant figures:

Since z=14y and z=1386 we have 14y=1386. Then $\displaystyle{y}=\frac{{1386}}{{14}}={99}$ .

Now $\displaystyle\sqrt{{{y}}}={2}{x}=\Rightarrow\sqrt{{{99}}}={2}{x}$ .

$\displaystyle{3}\sqrt{{{11}}}={2}{x}$

$\displaystyle{x}=\frac{{3}}{{2}}\sqrt{{{11}}}$

If you know how to extract square roots without a calculator, you will find that $\displaystyle\sqrt{{{11}}}\approx{3.317}$ so that $\displaystyle{x}\approx{4.98}$

This is a reasonable approximation as 2(4.98)=9.96; 9.96^2=99.2016; and 14(99.2016=1388.8224 which is close to the expected 1386.

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Friday, September 3, 2010