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Integers and Square Roots

A. How many integers are there between 5 and 14?

B. How Many rational numbers are there between 5 and 14?

C. One eighth of the square root of 7 less than a number is 2. What is the number?

D. x varies directly as the square of s and inversely as t. How does x change when s is doubled? When both s and t are doubled?

Solution Preview

A. The integers between 5 and 14 are 6, 7, 8, 9, 10, 11, 12 and 13 which are 8 in number.

B. We know 5 < 14 ==> 5+5 <5+14 ==> 5< (5+14)/2.
Similarly 5<14==>5+14<14+14==>(5+14)/2<14. Hence we can conclude that the rational number (5+14)/2 lies between 5 and 14. Generalizing, we can say that ...

Solution Summary

Integers and Square Roots are investigated. The solution is detailed and well presented.

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