Addition and Subtraction of Rational Numbers

Q.

Prove that $3+2\sqrt{5}$ is irrational

Q.

Prove that $5-\sqrt{3}$ is irrational

Q. The value of $\frac{3}{5}\times (\frac{35}{24}+\frac{10}{1})$ is _____.

1. $\frac{8}{55}$
2. $6\frac{7}{8}$
3. $5\frac{7}{8}$
4. $6\frac{5}{8}$

Q.

Prove that $4-5\sqrt{3}$ is irrational

Q. If y is the reciprocal of rational number x, then the multiplicative inverse of y will be _________.

1. $x$
2. $y$
3. $\frac{x}{y}$
4. $\frac{y}{x}$

Q.

Which of the following statements is incorrect?

1. Addition of any two irrational numbers can be rational.

2. Division of any two integers is an integer.

3. If 'a' is a rational number and 'b' is irrational, then a + b is irrational.

4. The product of a non-zero rational number with an irrational number is always irrational.

Q.

Simplify $\frac{{27}^{\frac{2}{3}}}{9^{\frac{1}{2}}{3}^{\frac{3}{2}}}$

Q. What is the additive identity of irrational numbers?

1. 1
2. 0
3. pi
4. 2

Q.

If $x$ and $y$ are distinct rational numbers which of the following is true about $\frac{x+y}{2}$?

1. greater than both x and y

2. less than both x and y

3. between x and y

4. less than x and greater than y

Q.

Which are the following are proper fractions?

$\frac{3}{5}$

Q.

Which are the following are the proper fraction?

$\frac{9}{13}$

Q.

For $\sqrt{3}{x}^2$ to be irrational, x should be

1. irrational or rational.

2. cannot be determined.

3. always rational.

4. always irrational.

Q. Match the two points to the distance between them.

1. $\frac{9}{2}$
2. $\frac{11}{2}$
3. $\frac{13}{2}$
4. $\frac{7}{2}$

Q.

Which are the following are the proper fraction?

$\frac{2}{17}$

Q. The product of a non-zero rational number with an irrational number is always an irrational number.

1. True
2. False

Q.

Which are the following are the proper fraction?

$\frac{8}{16}$

Q.

Prove the following number is irrational/not rational: $5+3\sqrt{2}$

Q.

State true or false.
If $x,y$ are rationals, then $x+y$ is a rational.

1. True

2. False

Q.

$(3+\sqrt{5})(3+\sqrt{5})$ is ___.( irrational/rational)

Q.

$(3+\sqrt{5})(3+\sqrt{5})$ is rational.

1. True

2. False

Q.

For $\sqrt{3}{x}^2$ to be irrational, x should be

1. always rational.

2. irrational or rational.

3. always irrational.

4. cannot be determined.

Q. Which of the following is a rational function?

1. $\frac{1}{3}\sqrt{4x^3+4x+7}$
2. $\frac{3x^5+5x^3+2x+7}{x^{3/2}},x>0$
3. $\frac{\sqrt{1+x}}{2+5x},x\ne -2/5$
4. $\frac{3x^3-7x+1}{x-2},x\ne 2$

Q. Find two rational number between $-3$ and $-2$.

Q. $5-\sqrt{2}\text{is irrational.}$

1. False
2. True

Q.

How many rational numbers can be determined between $\frac{3}{5}and\frac{7}{8}$.

Q. Find the distance between the points $2\frac{1}{2}$ and $5\frac{1}{4}$ on the number line.