Which is an irrational number? 1) Vo 2) 3.14 3) 3 3 4) 4

Which number is an irrational number? -10 o 19 V17 5,499

8. Look at this calculator screen.OF MATH TT 3.141592654 a) Is the number 3.141 592 654 rational or irrational? Explain. b) Is the number T rational or irrational? Explain your answer.

12. Circle the irrational number and explain what makes it irrational.(a) 43/2 (b) 3-2 (c) 31/2 (d) 9-1/2

pls answer this i need this asap :) (thank you in advance!)

. How many solutions using nonnegative integers are there to the equation x + y + z = 10? - 60 72 132 66

Another Field We'll let Q(√2) represent the set of numbers that can be written in the form a+b√2, where 'a' and 'b' and rational numbers (i.e., 'a' and 'b' are from 13 2 the set Q). For example, +¹3√2, 7.2-6√2, and 15 (= 15 + 0√2) are three numbers that would be in the set Q(√2), but √√3+ 4√2 or 3 + √2 would not be in the set Q(√2) (neither √√3 nor are rational numbers). A number such 3+5√2 would be in the set Q(√2) since 3+√2 can be re-written in the form 7 a+b√2 using the following steps: 7 7 3-5√2 21-35√2 21-35√2 21 - 35√2 21 35 == + √2 3+5√2 3+5√2 3-5√2 9 - 25(2) -41 41 41 = * Your task: Show that the system (Q(√2), +, *) is a field, where + is the ordinary addition operation and * is the ordinary multiplication operation. So, you need to show that: a. (Q(√2), +, *) is a commutative ring, and b. (Q(√2) - {0}, *) is a group.