Core Connections Integrated II, 2015
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Core Connections Integrated II, 2015 View details
2. Section 6.2
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Exercise 53 Page 340

Practice makes perfect
a Any sum or product that is rational can be rewritten as a fraction ab, where a and b are integers. Notice that 9 is a perfect square, which means we can simplify this radical to a number. With this information, we can simplify the expression.
sqrt(9)+5/17
3+5/17
51/17+5/17
56/17
Since we were able to rewrite the expression as a fraction ab where a and b are integers, this is a rational number.
b The symbol π is a symbol that denotes a decimal number with infinite non-repeating decimals.

Ď€ =3.14159265... Therefore, if we try to rewrite this sum as a fraction, the numerator will never be an integer. This means this is an irrational number.

c Any square root where the radicand is not a perfect square, such as 4, 9 or 16, will have infinite non-repeating decimals. Since 11 is not a perfect square, and we cannot rewrite the product, this must be an irrational number.
d Similar to Part C, we see a square root that is not a perfect square, sqrt(3). However since it is multiplied by a second square root, sqrt(12), we can rewrite this as a single square root and then simplify.
sqrt(12)* sqrt(3)
sqrt(36)
sqrt(6^2)
6
6/1
Since we were able to rewrite the expression as a fraction ab where a and b are integers, this is a rational number.