Which statement is true?
A.every realy number is an integer
B.every rational number is a real number
C.every rational number is a perfect square
D.every integer is an irrational number
An estimate for ✔️47 is between
A.4&5
B.5&6
C.6&7
D.7&8
An estimate for -✔️72 is
A.-8.1
B.-8.5
C.-9.1
D.-9.5
6 * 6 = 36
7 * 7 = 49
In order to find the correct answers to these questions, let's go through each statement and estimation problem individually:
1. Which statement is true?
a. Every real number is an integer.
b. Every rational number is a real number.
c. Every rational number is a perfect square.
d. Every integer is an irrational number.
To determine which statement is true, we can evaluate each one:
a. Every real number is an integer: This statement is not true because real numbers encompass a wide range of numbers, including non-integer values. So, a is false.
b. Every rational number is a real number: This statement is true. Rational numbers are numbers that can be expressed as a ratio of two integers, and they are a subset of real numbers. Therefore, b is true.
c. Every rational number is a perfect square: This statement is not true since perfect squares are integers that can be squared to produce another integer. Rational numbers include fractions, decimals, and numbers that cannot be squared to produce an integer. So, c is false.
d. Every integer is an irrational number: This statement is not true because integers are a subset of rational numbers, not irrational numbers. Irrational numbers cannot be expressed as a fraction and include numbers such as √2 and π. So, d is false.
Therefore, the correct answer is option B: Every rational number is a real number.
2. An estimate for √47 is between:
a. 4 & 5
b. 5 & 6
c. 6 & 7
d. 7 & 8
To estimate the value of √47, we can find the two perfect square numbers that √47 lies between. The perfect squares closest to 47 are 36 (6^2) and 49 (7^2). Since √47 is closer to 49 than 36, we can estimate that √47 is between 6 and 7.
Therefore, the correct answer is option C: 6 & 7.
3. An estimate for -√72 is:
a. -8.1
b. -8.5
c. -9.1
d. -9.5
Similarly, we can estimate the value of -√72 by finding the two perfect square numbers that -√72 lies between. The perfect squares closest to 72 are 64 (8^2) and 81 (9^2). Since -√72 is closer to -81 than -64, we can estimate that -√72 is closest to -9.
Therefore, the correct answer is option C: -9.1.