Show that V3 +2/6 is an irrational number.

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: Find a counterexample to disprove the conjecture: "The square of a number is always greater than…

A:

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 √2 and √3

A: Topic = Algebra

Q: Select all numbers that are irrational. E NIO

A: Ans:

Q: nen 1/2 is a positive odd integer. ed

A:

Q: Show that if a positive integer is odd, then it's square is odd.

A: To show that if a positive integer is odd then its square is odd

Q: Show 2.5262626262626... is a rational number by expressing it as a ratio of two integers.

A: Show 2.526262626.... is a rational number by expressing it as a ratio of two integers as follows.

Q: How did early mathematicians discover that irrational numbers exist?

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Q: 1. Prove that the square root of 2 is not a rational number.

A: Definition of rational number : If x is a rational number then it can be written in the form of pq…

Q: Prove that there is no rational number whose square is 12.

A:

Q: Determine the value of n if one of the roots of 2x2 - 16x + n = 0 is 4- V7.

A: We will find out the required value.

Q: Use a calculator to find a rational number r such that |r − π2| < 10−4.

A: Consider the given information. |r − π2| < 10−4 The absolute the function is defined as.…

Q: Show that there is no rational number r satisfying 2r = 3.

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Q: Are the irrational numbers closed under multiplication?

A: Use closure property.

Q: How do you prove the cube root of two is irrational?

A: this prove done by contradiction

Q: Luna told her friends that she was thinking of a number with the same digit in the ones and the…

A: To determine a number with the same digit in the ones and the thousands place (odd or even).

Q: If k is a positive integer, prove the k root of 6 is irrational

A: Given:Given that k is apositive integer.To find:The kth root of 6 is Irrational.

Q: Prove by contradiction that, if n is a positive integer which is not a perfect square, the sqrt(n)…

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Q: Show that √17 is Irrational number

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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: √126

A: Given problem:- 126 is a rational or irrational number

Q: (c) Show that 3/2+ 2/3 is an algebraic number?

A:

Q: Prove: The product of an irrational number and a nonzero rational number is irrational.

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Q: If a rational number times an irrational number is

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Q: How many irrational numbers are there?

A: How many irrational numbers are there?

Q: Show that square root P is irrational where P is prime by using contradiction.

A:

Q: Why do these rational numbers have terminating decimal? 1/30, 1/32, 1/40, and 3/60.

A: The number is said to be terminating if its denominator is in form of 2x5y. Simplify each number and…

Q: perform the indicated operations involving rational numbers. Express final answers in reduced form.…

A: Given: 47÷16-21

Q: Establish that square root 2 is a rational number

A:

Q: Prove that there does not exist an irrational number whose square root is rational.

A: Since, (p/q)=p^2/q^2 is rational. The square of any rational is rational, hence no rational is the…

Q: How many positive integer solutions are there to x1 + x2 + x3 =15 ?

A: From the given information we want to find How many positive integer solutions are there to x1 + x2…

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: 7x =4 (mod 12).

A:

Q: There is no integer that has a reciprocal that is an integer.

A: As per the instructions, we will be answering only the first question. For (32), Notice that the…

Q: Show that the following number is rational by writing it as a ratio of two integers. 2 +

A: Given                   29+25 So we know that rational number is in form of pqand where q is not…

Q: Express the following using factorials: 10 x 9 x 8 x 7

A: Meaning of factorial of a natural number : Suppose n is a natural number then meaning of n! is…

Q: Prove that there exists an irrational number whose square is rational.

A: We have to show that there exists an irrational number whose square is rational

Q: Show that 5 – V7 is an algebraic number.

A:

Q: If an irrational number is decreased by 2V18 result is V2. What is the number? V50, the

A: To find An irrational number when it is decreased by 218-50 and result…

Q: Use Proof by Contradiction to prove that the sum of an irrational number and a rational numbe is…

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Q: Prove that √7 is an irrational number.

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Q: Show that the product of a non-zero rational and an irrational is irrational.

A: A number 'a' is said to be rational if 'a' can be written as,pq where p, q≠0 are integers. And, a…

Q: 1. Joseph wants to find the side length of a square that has an area of 150 feet. Should his answer…

A:

Q: How many integer solutions are there to 1 +X2+X3+X4+Xs=31 with

A: Given, x1+x2+x3+x4+x5=31 Number of Solutions when xi≥0 and xi>0.

Q: What is the contrapositive of the statement “ A rectangle R with side lengths 1 and x, where x is…

A: theory Indeed, the ratio between length and width must be rational, even if we don't require the…

Q: Find a number that provides a counterexample to show that the given statement is false.

A: We have to find counter example for each of the given statement.

Q: A(n) ______ number is a real number that cannot be expressed as a ratio of two integers

A: