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. `sqrt(y)=2x ` . 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 `y=1386/14=99 ` .

Now `sqrt(y)=2x ==> sqrt(99)=2x ` .

`3sqrt(11)=2x `

`x=3/2sqrt(11) `

If you know how to extract square roots without a calculator, you will find that `sqrt(11)~~3.317 ` so that `x~~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.