Math - Real number system study guide.

Square roots will ALWAYS, NEVER, OR SOMETIMES be irrational numbers?

Sometimes.

Evaluate -5 to the 3rd power.

-125.

Create an example of a rational value between -8 and -9.

-8.67.

Evaluate (2/3) to the power of 2.

4/9.

Create an example of a irrational value between 2 and 3.

7 squared or 2.64.

Ricky ran 7/16 of a mile before stopping to tie his shoe. Represent the distance he ran as a decimal. Then, state if the decimal is terminating or repeating.

7/16 as a decimal equals 0.4375, which is a terminating decimal.

70 squared is is rational or irrational? Why?

Irrational because it isn't a perfect square.

The square roots of perfect squares will NEVER, ALWAYS, OR SOMETIMES be irrational numbers?

Never.

Are the following values in order from greatest to least? 3pi, 4 and then 5 squared, 5 and then 4 squared.

No.

-121 squared is rational or irrational? Why?

Rational because it is a perfect square.

2 and then 49 squared.

equals 14.

Between which two whole numbers does 150 lie?

12 and 13.

Which is true? 7 is less than 65 squared less than 0.8 2 is less than 7 squared less than 3 10 is less than 95 squared less than 11 13 is less than 160 less than 14

2 is less than 7 squared less than 3.

Which of the following is an example of an irrational number between 6 and 7? 2pi, 6.875, 32 squared, Both A and C, or All of the above?

2pi.

Emily ended up using 7/3 cups of flour in a recipe for cookies. Express the amount of flour that she used as a decimal. Then, state if the decimal is terminating or repeating.

7/3 in decimal form equals 2.3 repeating, so this is a repeating decimal.

Repeating decimals will ALWAYS, NEVER, OR SOMETIMES be rational numbers?

Always.

In the middle of a park, there is a fenced off area in the shape of a square with an area of 225 square yards. (A.) What is the side length of the square? (B.) What is the perimeter of the fenced off area?

(A.) 15 because you need to square 225. (B.) 60 because you take what the square root of the area is which is 15 and multiply it by the amount of sides the shape has, so you would multiply 15 and 4 to get 60.

Evaluate 10 to the 3rd power.

1,000.

Solve. x to the power of 2 = 900.

1/450.

Solve. p to the 3rd power = 27.

1/9.

Give an example of a fraction that could be represented as a repeating decimal.

Any fraction over 9 is considered a repeating decimal, so 1/9 is an example as it equals 0.1 repeated.

Give an example of a fraction that could be represented as a terminating decimal.

Any number over 10 would be an example of a terminating decimal, so 1/10 would be an example as it equals 0.1.

Which of the following is an example of a rational number between 7 and 8? 7.83 repeated, 52 squared, 7 1/9, both A and C, or All of the above.

Both A and C.

Choose the correct statement. 4 + 15 squared is GREATER OR LESS THAN 3 + 6 squared.

Greater than.

Choose the correct statement. 95 squared is GREATER OR LESS THAN 9.22 repeated.

Greater than.

0.72 repeated is rational or irrational? Why?

Rational because it is a repeating decimal.

0.87 is rational or irrational? Why?

Rational because it is a terminating decimal.

19/99 is rational or irrational? Why?

Rational because it is written as a fraction and and when you put it in decimal form it is a repeating decimal.

Express 0.15 repeated as a fraction in simplest form.

Since their are 2 digits in 0.15 repeated you put it over 2 9's which is 15/99, then you simplify and get 5/33 as your answer.

Express 0.125 as a fraction in simplest form.

Since their are 3 digits in 0.125, you have to put it over 1,000 and then simplify, so the answer would be 1/8 because you can divide 125 by itself and get 1 and then divide 1,000 by 125 and get 8.

Express -0.4 as a fraction in simplest form.

Since their is 1 digit in 0.4 you put it over 10, then you have to simplify, so you can divide the numerator and denominator by 2 and get -2/5.

Express 0.5 repeated as a fraction in simplest form.

Since their is one digit in 0.5 repeated you put it over one 9 and then you simplify, 5/9 can't be simplified any further so that is your answer.

Are the following values in ascending order? -3/2 -2 and 2 squared, -pi.

Yes.

A square sandbox has an area of 75 square feet. Estimate the length of one of the sides of the sandbox.

You find the square root of 75 and that is your answer so the answer would be 8.66.

Which of the following real numbers has the greatest value? 13.09 13 1/5 169 squared 13.1 repeated

You have to convert all of the choices into decimals and then decide from there, so the one with the greatest value is 169 squared.

Which of the following real numbers has the smallest value? 7.1 6pi 20/3 51 squared

You have to convert all of the choices into decimals and then decide from there, so the one with the smallest value is 20/3.

Willa purchases a vase for her kitchen that is shaped like a cube and will hold 343 cubic inches of water. What are the dimensions of the vase?

You have to find the cube root of 343, which is 7.

The square pool at Sammie's gym has an area of 144 square feet. What is the length of one side of the pool?

You need to square 144 and that equals 12, which is your answer.

Alaina bought a square frame for her desk that has an area of 81 square inches. What is the perimeter of the frame?

You need to square 81 which is 9, and then since it is a square it has 4 sides so you would multiply 9 and 4 and then you would get 36, which is your answer.

10 + 169 squared.

equals 23.

negative 100 squared.

equals negative 10.