Operations on Irrational Number

Q.

Sum of $2\sqrt{2}+5\sqrt{3}$ and $\sqrt{2}-3\sqrt{3}$ is

1. $2\sqrt{2}+3\sqrt{3}$

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

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

4. $3\sqrt{2}+\sqrt{3}$

Q. Question 13
$\frac{1}{\sqrt{9}-\sqrt{8}}$ is equal to

A) $\frac{1}{2}(3-2\sqrt{2})$
B) $\frac{1}{3+2\sqrt{2}}$
C) $3-2\sqrt{2}$
D) $3+2\sqrt{2}$

Q.

The greater number among $\sqrt{17}-\sqrt{12}$ and $\sqrt{11}-\sqrt{6}$ is

1. $\sqrt{17}-\sqrt{12}$

2. $\sqrt{11}-\sqrt{6}$

3. Can't be compared

4. Both are equal

Q.

$\frac{\sqrt{3}-1}{\sqrt{3}+1}=a-b\sqrt{3}$ then the values of a and b are

1. $a=1,b=2$

2. $a=2,b=1$

3. $a=2,b=3$

4. $a=3,b=2$

Q.

Multiplication of $6\sqrt{5}$ and $2\sqrt{5}$ is

1. 60

2. 40

3. 200

4. 300

Q.

Which of the following statement is incorrect?

1. The product of two rational numbers is always a rational number

2. Irrational numbers form part of the number line

3. The sum of two irrational numbers is always an irrational number

4. The sum or difference of a rational and an irrational numbers is irrational

Q.

State whether the following statements are true or false. Justify your answer.

(i) Every irrational number is a real number.
(ii) Every point on the number line is of the form $\sqrt{m}$, where m is a natural number.

Q.

Divide: $18\sqrt{21}$ by $6\sqrt{7}$.

Q.

Find the value of $(\sqrt{5}+\sqrt{2})(\sqrt{5}-\sqrt{2})$.

1. $2$

2. $3$

3. $4$

4. $1$

Q.

A set of natural numbers is finite or not.

Q.

Which of the following fraction is equal to $\frac{1}{\sqrt{5}-\sqrt{7}}$?

1. $\frac{-(\sqrt{5}+\sqrt{7})}{4}$

2. $\frac{-(\sqrt{5}+\sqrt{7})}{2}$

3. $\frac{-(\sqrt{5}-\sqrt{7})}{2}$

4. $\frac{-(\sqrt{5}+\sqrt{7})}{4}$

Q.

Division of $8\sqrt{15}$ by $2\sqrt{3}$ is

1. $4\sqrt{5}$

2. $4\sqrt{3}$

3. $\sqrt{5}$

4. $2\sqrt{5}$

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

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

Q. Question 11
$\sqrt{10}\times \sqrt{15}$ is equal to

A) $6\sqrt{5}$
B) $5\sqrt{6}$
C) $\sqrt{25}$
D) $10\sqrt{5}$

Q. Express the following with rational denominator:

$\left(i\right)\frac{1}{3+\sqrt{2}}$

Q. Express the following with rational denominator:

$\left(vii\right)\frac{6-4\sqrt{2}}{6+4\sqrt{2}}$

Q. Solve $p\left(x\right)=x^2+2\sqrt{2}x-6$

Q. The greater number between $\sqrt{17}-\sqrt{12}$ and $\sqrt{11}-\sqrt{6}$ is ____.

1. $\sqrt{17}-\sqrt{12}$
2. $\sqrt{11}-\sqrt{6}$
3. Both are equal
4. Cannot comare

Q.

Q.

Which of the following statements are incorrect?

1. The sum, product, division of two rational numbers is always a rational number

2. The sum, difference, product, division of two irrational number is an irrational number

3. Irrational numbers can be represented on the number line

4. The sum or difference of a rational number and an irrational number is irrational

Q. Say True or False
If $a$=$\sqrt{2}$ and $b$=$\sqrt{3}$ and $c=\sqrt{5}$
then does it satisfy the following property $(a+b)+c=(b+c)+a$

1. True
2. False

Q. Give an example of two irrational numbers, whose product is an irrational number.

1. $\sqrt{3},\sqrt{3}$
2. $\sqrt{2},\sqrt{2}$
3. $\sqrt{2},-\sqrt{2}$
4. $\sqrt{2},\sqrt{3}$

Q. Solve $\frac{x+\sqrt{x^2-1}}{x-\sqrt{x^2-1}}+\frac{x-\sqrt{x^2-1}}{x+\sqrt{x^2-1}}=98.$

1. $\pm 1$
2. $\pm 5$
3. $\pm 4$
4. $\pm 10$

Q. Evaluate $\frac{\sqrt{5}}{\sqrt{3}+\sqrt{2}}-\frac{3\sqrt{3}}{\sqrt{5}+\sqrt{2}}+\frac{2\sqrt{2}}{\sqrt{5}+\sqrt{3}}$

Q. Find the value of $\sqrt[5]{516}\times \sqrt[5]{52}$.

Q. Every rational number is

1. A natural number
2. An integer
3. A real number
4. A whole number

Q.

Find the values of $a$ and $b$

if $\frac{5+2\sqrt{3}}{7+4\sqrt{3}}=a+b\sqrt{3}$

1. $a=11,b=-6$

2. $a=9,b=-6$

3. $a=-11,b=6$

4. $a=-9,b=6$

Q. In a 5 km marathon, Manish ran 2 km. If Kushagra ran $\frac{1}{2}$ of the total distance of the marathon, who ran more?

Q.

Which of the following fractions is equal to $\frac{1}{\sqrt{3}-\sqrt{5}}$?

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

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

3. $\frac{-(\sqrt{3}-\sqrt{5})}{2}$

4. $\frac{(\sqrt{3}+\sqrt{5})}{4}$

Q.

The value of $(5+\sqrt{7})(2+\sqrt{5})$ is

1. $10+5\sqrt{5}+2\sqrt{42}$

2. $10+10\sqrt{47}$

3. $10+5\sqrt{5}+2\sqrt{7}+\sqrt{35}$

4. $10+10\sqrt{12}+\sqrt{35}$