Operations on Irrational Numbers

Q.

Add (i) $(2\sqrt{3}-5\sqrt{2})and(\sqrt{3}+2\sqrt{2})$

(ii) $(2\sqrt{2}+5\sqrt{3}-7\sqrt{5})and(3\sqrt{3}-\sqrt{2}+\sqrt{5})$

(iii) $(\frac{2}{3}\sqrt{7}-\frac{1}{2}\sqrt{2}+6\sqrt{11})and(\frac{1}{3}\sqrt{7}+\frac{3}{2}\sqrt{2}-\sqrt{11})$

Q.

Find the irrational numbers between root 2 and root 3

Q.

Find two irrational numbers between √3 and √5

Q.

How to find irrational numbers between any two irrational or a rational number

Q.

How to find irrational number between any two numbers

Q.

Is √361 rational or irrational ?

Why?

Q.

Find 3 irrational numbers between 4 and 5

Q.

What is the square root of $\frac{25}{36}$?

Q.

An irrational number between 2 and 3 is____

1. Sq root 2

2. Sq root 3

3. Sq root 4

4. Sq root 6

Q.

The value of $\sqrt{20}\times \sqrt{5}$ is,

(a) 10

(b)$3\sqrt{5}$

(c)$5\sqrt{5}$

(d)$3\sqrt{3}$

Q. Statement 1: The sum of a rational number and an irrational number may or may not be irrational.

Statement 2: The difference of two irrational numbers may or may not be irrational.

1. Both statement 1 and statement 2 are true.
2. Statement 1 is false, while statement 2 is true.
3. Statement 1 is true, while statement 2 is false.
4. Both statement 1 and statement 2 are false.

Q.

Find two irrational numbers between 0.61611611116......., and 0.6835452935

Q. Which of the following will result in a rational number?​

1. $7\sqrt{5}-2\sqrt{5}$
2. $4\sqrt{3}\times (-2\sqrt{12})$
3. $4\sqrt{7}+\sqrt{7}$
4. $9\sqrt{6}÷3\sqrt{2}$

Q.

Fill in the following boxes:

$\frac{2}{\square }=\frac{4}{10}=\frac{\square }{25}=\frac{8}{\square }$

Q. Find the values of a and b if
$\frac{7+\sqrt{5}}{7-\sqrt{5}}-\frac{7-\sqrt{5}}{7+\sqrt{5}}=a+\frac{7}{11}\sqrt{5}b$

Q.

Which of the following is the rationalising factor of $3-7\sqrt{2}$

1. 3 + 2√7

2. -3 - 7√2

3. 3 + 7√2

4. -3 + 7√2

Q. Find the square root of the following
i. 9801
ii. 2079.36
iii.$\frac{2\sqrt{1337}}{3844}$
iv.$\frac{\sqrt{59.29}-\sqrt{5.29}}{\sqrt{59.29}+\sqrt{5.29}}$

Q.

Find the square of $\sqrt{3}+\sqrt{2}$

1. $5+2\sqrt{2}$

2. $5-2\sqrt{6}$

3. $15+2\sqrt{6}$

4. $5+2\sqrt{6}$

Q. An irrational no. lying between √4 & 5 is (1) √10÷2 (2) √5÷2 (3) √10 (4) √20÷4

Q. Find the values of a and b if
$\frac{7+\sqrt{5}}{7-\sqrt{5}}-\frac{7-\sqrt{5}}{7+\sqrt{5}}=a+\frac{7}{11}\sqrt{5}b$

[ 3 marks ]

Q. The decimal expansion of a number $\frac{p}{q}$ was found to be 2.444... . Find the value of p + 2q.

1. 11
2. 13
3. 10
4. 16

Q.

Fill in the following boxes:

$\frac{3}{10}=\frac{12}{\square }=\frac{\square }{50}=\frac{\square }{60}$

Q. An irrational no. lying between √4 & 5 is (1) √10÷2 (2) √5÷2 (3) √10 (4) √20÷4

Q. find one irrational number and one rational number between 2 and root5

Q. The result of $(3+\sqrt{5})\times$, is a rational number.

1. $\sqrt{5}$
2. 3
3. $(3+\sqrt{5})$
4. $(3-\sqrt{5})$

Q. The square root of sum of the digits in the square of $121$ is

1. $4$
2. $3$
3. $6$
4. $9$

Q.

Fill in the following boxes:

$\frac{1}{2}=\frac{8}{\square }=\frac{\square }{10}=\frac{6}{\square }$

Q. What are the values of a and b if:

$\frac{7+\sqrt{5}}{7-\sqrt{5}}-\frac{7-\sqrt{5}}{7+\sqrt{5}}=a+\frac{7}{11}\sqrt{5}b$

Q. find two rational and irrational number between 1 by 3 and 1 by 7