The expressions are irrational 1/3 + √216 and √64+ √353 and the expressions √100 × √100, 13.5 + √81, √9 + √729, and 1/5 + 2.5 are rational number.
<h3>What is a rational number?</h3>
If the value of a numerical expression is terminating then they are the rational number then they are called the rational number and if the value of a numerical expression is non-terminating then they are called an irrational number.
1. √100 × √100
→ √100 × √100
→ 10 × 10 = 100
This is a rational number.
2. 13.5 + √81
→ 13.5 + √81
→ 13.5 + 9 = 22.5
This is a rational number.
3. √9 + √729
→ √9 + √729
→ 3 + 27 = 30
This is a rational number.
4. √64+ √353
→ √64 + √353
→ 8 + √353
This is an irrational number.
5. 1/3 + √216
→ 1/3 + √216
→ 1/3 + √216
This is an irrational number.
6. 1/5 + 2.5
→ 1/5 + 2.5
→ 0.2 + 2.5 = 2.7
This is a rational number.
More about the rational number link is given below.
brainly.com/question/9466779
If the integers have the same absolute value ... they're the same number
but with different signs ... then their sum is zero.
Example: (plus) 927 added to (negative) 927 = zero
If the integers have different absolute values ... they're different numbers with different
signs ... then their sum has the same sign as the one with the bigger absolute value.
Examples:
==> (plus) 92 added to (negative) 91
92 and 91 are 1 number apart on the number line.
The positive number is bigger than the negative number.
So the sum is +1 .
==> (plus) 35 added to (negative) 37
35 and 37 are 2 numbers apart on the number line.
The negative number is bigger than the positive one.
So the sum is -2 .
Answer:
∑ (-1)ⁿ⁺³ 1 / (n^½)
∑ (-1)³ⁿ 1 / (8 + n)
Step-by-step explanation:
If ∑ an is convergent and ∑│an│is divergent, then the series is conditionally convergent.
Option A: (-1)²ⁿ is always +1. So an =│an│and both series converge (absolutely convergent).
Option B: bn = 1 / (n^⁹/₈) is a p series with p > 1, so both an and │an│converge (absolutely convergent).
Option C: an = 1 / n³ isn't an alternating series. So an =│an│and both series converge (p series with p > 1). This is absolutely convergent.
Option D: bn = 1 / (n^½) is a p series with p = ½, so this is a diverging series. Since lim(n→∞) bn = 0, and bn is decreasing, then an converges. So this is conditionally convergent.
Option E: (-1)³ⁿ = (-1)²ⁿ (-1)ⁿ = (-1)ⁿ, so this is an alternating series. bn = 1 / (8 + n), which diverges. Since lim(n→∞) bn = 0, and bn is decreasing, then an converges. So this is conditionally convergent.
Answer:
10
Step-by-step explanation:
half of 10 is 5
The answer is 14 dollars because 56 divided by 4 gives 14
