Irrational Numbers

Q.

Which of the following is not an irrational number?

1. $5-\sqrt{3}$

2. $4+\sqrt{2}$

3. $5+\sqrt{9}$

4. $5+\sqrt{3}$

Q. what does non integer rational number mean? is it fractions ?

Q.

The number ${(1+\sqrt{3})}^2$ is a/an

1. Natural Number

2. Rational Number

3. Irrational Number

4. Integer

Q.

$\pi$ =$\frac{22}{7}$. Is it true or false

1. True

2. False

Q. The square root of a prime number is always irrational.

1. False
2. True

Q. If $x^{x\sqrt{x}}={\left(x\sqrt{x}\right)}^x$, find the value of $x$.

1. $\frac{3}{2}$
2. $\frac{2}{9}$
3. $\frac{4}{9}$
4. $\frac{9}{4}$

Q. If a number P is a positive integer but not a perfect square, then $\sqrt{P}$ is definitely _________.

1. An integer
2. A rational number
3. An irrational number
4. A terminating decimal number

Q. 15. Find a irrational number between 0.1 and 0.2.

Q. Between $\mathrm{1.7320508...}$ and $\mathrm{0.333...}$, which is the rational and which is the irrational number?

1. Both are irrational numbers
2. $\mathrm{1.7320508...}$ is irrational number, while $\mathrm{0.333...}$ is rational number
3. Both are rational numbers
4. None of the above

Q. Which of the following numbers have an irrational number square root?

1. $625$
2. $6025$
3. $3025$
4. $1225$

Q.

Write the following rational numbers in decimal form and find out the block of repeating digits in the quotient.

$\frac{1}{3}$

Q. Upon adding a rational number and an irrational number, we get a/an ______ number.

1. irrational
2. whole
3. negative
4. rational

Q.

If 1K × K1 = K2K, the letter K stands for the digit

A. 1

B. 2

C. 3

D. 4

Q. Irrational numbers can be located on the number line using Pythagoras' theorem.

1. False
2. True

Q.

The ratio of the circumference of a circle to the diameter of the circle is.

1. An irrational number

2. A rational number

3. An integer

4. A whole number

Q. The rational and the irrational numbers together constitute the ______ numbers.

1. integer
2. natural
3. whole
4. real

Q. Which among the following has a non-terminating non-repeating decimal expansion?

1. $\pi$
2. $\frac{10}{3}$
3. $\frac{22}{11}$
4. $\frac{22}{4}$

Q. The $\frac{p}{q}$ form of $0.\overline{18}$ is (where p and q are integers and $q\ne 0$) .

1. $\frac{2}{22}$
2. $\frac{2}{11}$
3. $\frac{2}{33}$

Q.

Examine whether the following number is rational or irrational:

$5.040040004...$

Q. Select all the irrational numbers

1. $0.256789$
2. $1.376871\dots$
3. $0.166666\dots$
4. $\frac{1}{10}$
5. $4.398235\dots$
6. $23$
7. $5.252908\dots$
8. $0$
9. $12.35689\dots$
10. $8.912913\dots$

Q. Choose the option that has at least one irrational number.

1. $\sqrt[3]{3216},\frac{1}{9}$
2. $\frac{–13}{9},\sqrt{12\times 27}$
3. $\frac{3\pi }{16\pi },\frac{29}{7}$
4. $\sqrt{45},\sqrt{2\times 98}$

Q. Upon adding a rational number and an irrational number, we get a/an ______ number.

1. rational
2. irrational
3. negative
4. whole

Q. Irrational numbers can be exressed as $\frac{p}{q}$, where $p$, $q$ are integers and $q\ne 0$

1. No
2. Yes

Q. The rational and the irrational numbers together constitute the ______ numbers.

1. whole
2. natural
3. integer
4. real

Q. Estimate $\sqrt{623}$ to its nearest whole number.

1. 24
2. 25
3. 26
4. 23

Q. Find the number of digits in the square root of 2043.04

1. 3
2. 2
3. 5
4. 4

Q. The rational and the irrational numbers together constitute the ______ numbers.

1. natural
2. integer
3. real
4. whole

Q. The product of two irrational numbers is ____.

1. irrational
2. rational
3. rational or irrational
4. whole

Q. If $\sqrt{2^n}=1024$ , then $3^{\left(\frac{n}{4}-4\right)}$ =________

1. $3$
2. $-3$
3. $27$
4. $81$

Q. Which of the following is a rational number but not a fraction?

1. -4
2. $\frac{5}{2}$
   
3. 4
4. $\frac{1}{3}$