Operations on Monomial Surds

Q.

Sum/Difference of a rational and irrational number is a rational number

1. True

2. False

Q. Is $\pi$ rational or irrational?

Q.

The simplest form of $\frac{\sqrt[4]{4243}}{\sqrt[4]{43}}$ is

1. $3$

2. $4$

3. $2$

4. $9$

Q.

Can the product of two irrational numbers be rational? Explain your answer and support with an example.

Q. Question 3
Insert a rational number and an irrational number between the following
(i) 2 and 3
(ii) 0 and 0.1
(iii) $\frac{1}{3}$ and $\frac{1}{2}$
(iv) $\frac{-2}{5}$ and $\frac{1}{2}$
(v) 0.15 and 0.16
(vi) $\sqrt{2}$ and $\sqrt{3}$
(vii) 2.357 and 3.121
(viii) .0001 and .001
(ix) 3.623623 and 0.484848
(x) 3.375289 and 6.375738

Q.

Product of a rational and an irrational number is always rational.

1. False

2. True

Q. Define Irrational number?

Q. Simplify ($\sqrt{15}$+$\sqrt{13}$) ($\sqrt{15}$-$\sqrt{13}$)

[2 Marks]

Q.

$If{3}^a=729,then{3}^{a-2}=$

1. 27

2. 243

3. 81

4. 9

Q.

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

1. 32

2. $\sqrt[5]{518}$

3. 4

4. 2

Q. $\frac{6\sqrt{5}}{\sqrt{3}}$ can also be written as :

1. $2\sqrt{30}$
2. $4\sqrt{15}$
3. $2\sqrt{15}$
4. $6\sqrt{15}$

Q. Simplify : $\frac{\sqrt[4]{41024}}{\sqrt[4]{44}}$

1. 4
2. 2
3. 16
4. 64

Q.

Product of a non-zero rational and irrational number is always irrational

1. True

2. False

Q.

Which of the following statements are always true?

1. The sum of two irrational numbers is irrational.

2. Product of two irrational numbers is an irrational number.

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

4. The product and quotient of a non-zero rational and irrational number is irrational.

Q. Simplify
$\frac{2\sqrt{6}}{\sqrt{2}+\sqrt{3}}+\frac{6\sqrt{2}}{\sqrt{6}+\sqrt{3}}-\frac{8\sqrt{3}}{\sqrt{6}+\sqrt{2}}$

Q.

$\frac{2\sqrt{3}}{\sqrt{7}}=$ ___

1. $2\sqrt{21}$

2. $\frac{2\sqrt{7}}{\sqrt{3}}$

3. $\frac{2\sqrt{21}}{7}$

4. $1$

Q.

Choose the correct answer from the given four options .

The operation not involved in forming the expression $5x+\frac{5}{x}$ from the variable $x$ and number $5$ is

1. Addition

2. Subtraction

3. Multiplication

4. Division

Q. $\sqrt{3}$ is a/an

1. natural number
2. whole number
3. rational number
4. irrational number

Q.

$\sqrt{-2}=-\sqrt{2}$

1. True

2. False

Q. Find the value of ${({61}^2-{11}^2)}^{\frac{3}{2}}$

Q.

The value of $0.\overline{23}+0.\overline{22}$ is

1. 0.45

2. 0.78

3. $0.\overline{45}$

4. $0.\overline{23}$

Q.

If we subtract $\frac{1}{2}$ from a number and multiply the result by $\frac{1}{2}$, we get $\frac{3}{8}$. Then the number is ___.

Q. $\sqrt{3}$ is a/an _______ number.

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

Q.

Which one is in the simplest form for √112?

1. 6√7

2. 5√7

3. 8√7

4. 4√7

Q.

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

1. $\sqrt[5]{518}$

2. 32

3. 2

4. 4

Q.

When we divide two irrational numbers, we may or may not get a rational number.

1. True

2. False

Q.

If we subtract $\frac{1}{2}$ from a number and multiply the result by $\frac{1}{2}$, we get $\frac{3}{8}$. Then the number is ___.

Q. The value of ${\int }_1^4{\left\{x\right\}}^{\left[x\right]}dx$ (where $[.]$ and $\{.\}$ denotes the greatest integer and fractional part of $x$) is equal to

1. $\frac{11}{12}$
2. $\frac{13}{12}$
3. $\frac{7}{12}$
4. $\frac{19}{12}$

Q.

Which of the following statements are correct?

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.

The product of two irrational numbers is a/an

1. Irrational number

2. Rational number

3. Real number

4. All of the above