Is the sum of two irrational numbers always an irrationalnumber?

Q: Is there a real number whose square is-I

A: Square of any real number should be positive.

Q: plz solve q4

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Q: is the set of irrational numbers closed for: a) addition and b) multiplication

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Q: My question is The product of two integers will have the same sign as the quotient of the two…

A: The given statement is true always ,becauseLet take two numbers x and yCase I x and y both are…

Q: Is it possible to raise a positive number b to a power and obtain a negative number? Is it possible…

A: The given statement is " The possibility to raise a positive number b to a power and obtain a…

Q: show that SZ+5 is irrational number

A: If a number cannot be written in ab form, where a and b are integers is known as an irrational…

Q: every rational number is a decimal true or false?

A: We know that rational numbers are of the form of terminating and repeating decimals whereas…

Q: Find a Rational number between 1/4 and 1/3

A: We will use basic knowledge of rational numbers to answer this question.

Q: Find a rational number between √2 and √3

A: Topic = Algebra

Q: Computers can store integers exactly but not real numbers in general. Instead, they approximate them…

A: (e) floating point numbers We have to find out the reason that why real numbers cannot be stored in…

Q: Define the term domain of nonnegative numbers?

A: Non negative numbers are all real numbers that are 0 or greater than 0.

Q: Is the number z = 5 a pure imaginary number?

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Q: The sum of any two integers of the from 4k+ is always: a) prime b) zero c) Even

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Q: Show that the sum of the cubes of the first n positive integers is (n(n + 1)/2)^2

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Q: what is eight minus the absolute valueof two x plus nineis less than or equal to seven written in…

A: Given: We have to find the value of x such that we have given condition is  8-2x+9≤7

Q: Give an example of an irrational number that greater than 10:

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Q: Verify that for any three consecutive integers, the sum of the smallest and largest is equal to…

A: Given: Three consecutive integers.

Q: Is any real number exactly 1 less than its cube?

A: Is any real number exactly 1 less than its cube?

Q: Find three consecutive integers Such thate Hour times the sauare Of theo third less three times the…

A: Let consecutive integers are x-1,x,x+1

Q: Express 4 as sum of suares of two rational numbers

A: Let one rational number be = xSecond rational number be = yThen,According to question, the sum of…

Q: Are the irrational numbers closed under multiplication?

A: Use closure property.

Q: True or False The sum of the odd numbers is always an odd number.

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Q: Use direct proof to show that product of two consecutive integers is even.

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Q: Use deductive reasoning to create a procedure that will result to six times the original number.

A: 1. Consider the number x  2. multiply the number by 6 to get 6 times the number     Therefore, 6x 6x…

Q: Determine whether the statement Every decimal with a repeating pattern of digits is a rational…

A: Consider the given statement, Every decimal with a repeating pattern of digits is a rational number…

Q: What two nonnegative real numbers with a sum of 34 have the largest possible product?

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Q: is an even integer then n square is .A Negative

A: Suppose n=m is an even integer.Since n=m , then n2=m2

Q: Show that this number is Irrational number

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Q: If a rational number times an irrational number is

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Q: every two rational numbers there is an irrational number.

A: We have to prove the given statement that is '"between every two rational numbers there is an…

Q: Is there a real number whose square is – 1?

A: Given that, The number i.

Q: What does the set of real numbers consist of?

A: To discuss about real number

Q: Is there a positive real number “closest” to 0?

A: Suppose there is a positive real number closest to 0. Let it be a. Now the distance from 0 to a is…

Q: Prove: “The sum of two even integers is even.”

A: To prove: The sum of two even integers is even. n is an even number if it can be expressed as n =…

Q: Show that 3 + V5 is irrational number

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Q: The product of an irrational number and an irrational number is irrational. Always Sometimes Never

A: Given statement: Irational number×Irational number=Irational number

Q: The set of rational numbers is closed under division. True or False?

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Q: The sum of the squares of two odd integers is 1) Perfect 2) Prime 3) Not perfect

A: We will find out the required solution.

Q: Show that 2 + V5 is irrational number

A: To prove that 2+53 is irrational number. (It is evident that 2 is irrational, but here providing its…

Q: is there integer that has reminder of 2 when its devided by 5?

A: There are infinite number of integers that has reminder of 2 when its divided by 5

Q: what is the absolute value for a number that is positive

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Q: For which positive integers $n$ greater than or equal to 2 is $\sqrt[n]{a^{n}}=a$ always a true…

A: We need to check for all the values to get the result

Q: Suppose you divide a natural number n by a positive rational number less than 1. Will the answer…

A: Take a rational number x=p/q such that x belong to (0,1)

Q: Use a direct proof to show that the product of two odd numbers is odd.

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Q: Show that every odd integer is the sum of two consecutive integers

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Q: be a positive number. Determine the values of p for which

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Q: True or false, for any integer x, x^2, - x will always result in an even number

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Q: Are there numbers whose squares are smaller than the numbers themselves

A: To find number such that x2 < x.

Q: Find for the sum of the first 50 negative even integers.

A: Negative even integers :-    -2,-4,-6,-8, ....... This is AP series with a=-2, d=-2

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.