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

Q: 10. Show that the product of a+bi and b+ai always results in a purely imaginary number, given that a…

A: Given two complex numbers: a+bi and b+ai

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

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Q: What is a simple mathematical proof that the square root of 2 is irrational

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Q: Show that if ya – ay = 1 has no rational solution for positive a such that a is a natural number and…

A: The given equation is ya-ay=1,a≠2 this equation is not valid for a = 1 although it is given for…

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

A: Topic = Algebra

Q: Is there a real number whose square is –1? a. Is there a real number x such that _? such that x =…

A: In general, there does not exist any such real number whose square is a negative real number. Hence,…

Q: Based on the above information, conjecture if the statement is ALWAYS true. SOMETIMES true, or NEVER…

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Q: Show that the following number is rational by writing it as a ratio of two integers. 5.6057

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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: use proof by contradiction to show that the number is irrational. 4/11

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Q: The square root property indicates that if x2= k, then x = __________.

A: According to the given information it is required to tell that:The square root property indicates…

Q: . Prove that between every rational number and every irrational number there is an irrational…

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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: The volume of a 12-inch-tall cone is 144n cubic inches. Which statement about the radius of the base…

A: We are given the volume 'V' of the cone 144 π  cubic inches and the height 'h' of the cone 12 inch.…

Q: Show by contradiction that if 10x2+ 2 is irrational, then x is irrational. 5

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Q: 11. Prove that if n is a perfect square, then n + 2 is not a perfect square.

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

A: this prove done by contradiction

Q: Find the length of side x in simplest radical form with a rational denominator. 4 [coefficient] O 2…

A: Given figure is :   To find the value of x

Q: Prove that if a is an irrational number, then a-1 is an irrational number.

A: Given:           a is an irrational number To prove:            a-1 is an irrational number

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

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Q: If the rational number r is also an algebraic integer, prove that r must be an ordinary integer.

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Q: If a rational number times an irrational number is

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

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Q: Prove that if n is a perfect square, then n +2 is not a perfect square.

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Q: 1. 5.3535353, when expressed as a rational number, is:

A: we know the sum of infinite geometric  series  whose first term is  a and  whose common ratio is  r…

Q: ind the length of side x in simplest radical form with a rational denominato 45° 45 V3

A: By using trigonometry ratio, we find the value of 'x'.

Q: a. If p E P is a prime number, prove that the cube root of 2p is irrational.

A: We will use the basic knowledge of number theory and logic to answer this question. Note that only…

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

A: A rational number can be represented as pq, where p, q are integers and q≠0. If a number can not be…

Q: ind the length of side x in simplest radical form with a rational denominator.

A: Our Aim is to find the length of side x in the given triangle below:-

Q: Establish that square root 2 is a rational number

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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: a. Suppose that r E Q and r E Qª. Prove or disprove: The number (r – x)-1 e Qª. b. Prove or…

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Write a detailed proof for the statement: Between every two rational numbers there exists an…

A:

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: 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: 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: Prove that 13,050.046 is not the square of a natural number.

A: Use the fact that an even number is perfect square the number is divisible by 4

Q: Prove or disprove that if a and b are rational numbers, then ab is also rational.

A: we just give one example so that  a and b are rational but ab  is not rational

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

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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…

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Q: Show that 2 is a primitive root of 19.

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

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Power Operation

Power operation is topic of algebra in Math. It is use to represent repeated multiplication. Very big number and very small number can be easily express using power operation. Power operation is useful in many fields. In space engineering, it helps in representing the distance or size of particular heavenly body. In medical field, it is used to represent very small size. In medical field it helps to mention size of bacteria or virus. 

Exponents

The exponent or power or index of a variable/number is the number of times that variable/number is multiplied by itself.