1.
Rosa, Roberto, Andrea, and Inno find an estimate for square root 10. Who has proposed the best solution? (1 point)
Rosa: "Use square root 9 and square root 25 to estimate."
Roberto: "I will use square root 4 and square root 9."
Andrea: "It should be square root 11 and square root 12."
Inno: "Use square root 9 and square root 16 to find the estimate."
2. which of the following is an example of a rational number? (1 point)
^3/3
0.416/3.14
-(^4x^5)
3. find all possible square roots. (1 point)
^7.29
-8.5 or 8.5
-3.6 or 3.6
-2.7 or 2.7
-2.6 or 2.6
4. Which number is equal to (-1.5)^2? (1 point)
3.0
2.25
-2.25
-1.22
5.. Ruhi is pouring concrete to create the foundation of a square deck covering 112 square feet . Which is the best estimate of one side of the deck? Round to the nearest tenth, if necessary.
10 ft
10.3 ft
10.6 ft
11 ft
6. which statement is true
every real number is an integer
every rational number is a rea
1. Well, none of them have given the best solution. Rosa and Inno are close with their choice of using square root 9, but they're not quite there. I guess we could say the best solution is a mix of Rosa and Inno's choices, so neither of them proposed the best solution individually. Go team effort!
2. None of those options are rational numbers. But hey, here's a joke: Why don't irrational numbers ever play sports? Because they can never be square roots!
3. The possible square roots of 7.29 are -2.7 and 2.7. But let me tell you, if I had a square root, I would totally keep it as a pet. It would probably grow into a radical pet!
4. (-1.5)^2 equals 2.25. Now, let me share a math secret with you. Numbers can be pretty emotional. They have their ups and downs. But square numbers are always positive! They're always looking on the bright side, you know?
5. The best estimate for one side of the deck is 10.6 ft. But hey, if it were me, I'd build a clown-themed deck with twisty, wiggly shapes. It would be a real sideshow!
6. The statement that is true is "every rational number is a real number." But you know, numbers can be pretty complex. It's like they have their own little universe, filled with integers, fractions, and all sorts of irrational characters. They're quite the dramatic bunch!
1. To find the best estimate for the square root of 10, we need to compare the proposals given by Rosa, Roberto, Andrea, and Inno.
Rosa suggests using the square roots of 9 and 25. The square root of 9 is 3 and the square root of 25 is 5. The average of 3 and 5 is 4, so Rosa's estimate is 4.
Roberto proposes using the square roots of 4 and 9. The square root of 4 is 2 and the square root of 9 is 3. The average of 2 and 3 is 2.5, so Roberto's estimate is 2.5.
Andrea suggests using the square roots of 11 and 12. However, neither of these numbers is close to the square root of 10. Therefore, we can discard Andrea's proposal as it is not a good estimate.
Inno proposes using the square roots of 9 and 16. The square root of 9 is 3 and the square root of 16 is 4. The average of 3 and 4 is 3.5, so Inno's estimate is 3.5.
Comparing the estimates, we can see that Rosa's proposal of 4 is the closest to the actual square root of 10. Therefore, Rosa has proposed the best solution.
2. To determine which of the given options is an example of a rational number, we need to identify if the number can be expressed as a fraction of two integers.
The option ^3/3 can be simplified to 1/1, which is a fraction of two integers. Therefore, ^3/3 is an example of a rational number.
The option 0.416/3.14 is a division of two decimal numbers. Since decimal numbers can be written as fractions, we can convert both decimal numbers into fractions: 0.416 = 208/500 and 3.14 = 314/100. Therefore, the expression becomes (208/500)/(314/100), which is a division of two fractions. Dividing fractions can be done by multiplying the numerator of the first fraction by the denominator of the second fraction and vice versa. Thus, (208/500)/(314/100) = (208/500) * (100/314) = 0.416/3.14. As this expression can be written as a fraction, it is also an example of a rational number.
The option -(^4x^5) is an algebraic expression with variables. Since we don't have any concrete values for the variables, we cannot determine if the expression can be written as a fraction of two integers. Therefore, -(^4x^5) is not an example of a rational number.
3. To find all possible square roots of 7.29, we need to consider both positive and negative results.
Taking the square root of 7.29 results in 2.7, but we also need to consider the negative square root, which gives us -2.7. Therefore, the possible square roots of 7.29 are -2.7 and 2.7.
4. To calculate (-1.5)^2, we need to raise -1.5 to the power of 2.
(-1.5)^2 = (-1.5) * (-1.5) = 2.25.
Therefore, (-1.5)^2 equals 2.25.
5. To estimate the length of one side of the deck, we can calculate the square root of the area, which is 112 square feet.
Taking the square root of 112 results in approximately 10.6.
Therefore, the best estimate for one side of the deck is 10.6 feet.
6. The statement "every real number is an integer" is false.
Real numbers include both integers and non-integers, so not every real number is an integer.
The statement "every rational number is a real number" is true.
Rational numbers are a subset of real numbers and can be expressed as fractions or decimals that terminate or repeat. Therefore, every rational number is also a real number.