Arranging Irrational Numbers in the Ascending or Descending Form

Q.

Find the square root of $23$

Q. Arrange the numbers in decending order: $\sqrt{81},\sqrt{27},\frac{1}{\sqrt{3}},\sqrt{3}$

1. $\sqrt{81},\sqrt{27},\frac{1}{\sqrt{3}},\sqrt{3}$
2. $\frac{1}{\sqrt{3}},\sqrt{3},\sqrt{27},\sqrt{81}$
3. $\sqrt{81},\sqrt{27},\sqrt{3},\frac{1}{\sqrt{3}}$

Q. Compare the irrational numbers: $3,\sqrt[3]{38},\sqrt{2},\sqrt[3]{3125},\sqrt{31},6$

1. $6>\sqrt{31}>3>\sqrt[3]{38}>\sqrt{2}>\sqrt[3]{3125}$
2. $6>\sqrt{31}>\sqrt[3]{3125}>3>\sqrt[3]{38}>\sqrt{2}$
3. $6>3>\sqrt{31}>\sqrt[3]{38}>\sqrt{2}>\sqrt[3]{3125}$

Q. $\text{The numbers}2\sqrt{5},\frac{\sqrt{5}}{2},(\sqrt{5}{)}^3,\&\frac{5}{\sqrt{5}}$$\text{arranged in ascending order is}$

1. $\frac{\sqrt{5}}{2}<\frac{5}{\sqrt{5}}<2\sqrt{5}<(\sqrt{5}{)}^3$
2. $\frac{5}{\sqrt{5}}<\frac{\sqrt{5}}{2}<2\sqrt{5}<(\sqrt{5}{)}^3$
3. $\frac{\sqrt{5}}{2}<2\sqrt{5}<\frac{5}{\sqrt{5}}<(\sqrt{5}{)}^3$
4. $\frac{\sqrt{5}}{2}<\frac{5}{\sqrt{5}}<(\sqrt{5}{)}^3<2\sqrt{5}$

Q. Compare $\sqrt[3]{364},\sqrt[3]{380}$.

1. $\sqrt[3]{364}>\sqrt[3]{380}$
2. $\sqrt[3]{364}<\sqrt[3]{380}$
3. $\sqrt[3]{364}=\sqrt[3]{380}$
4. None of the above

Q. Which of the following is an approximate value of $\sqrt{60}$?

1. 7.45
2. 7.89
3. 8.1
4. 7.73

Q. Arrange $\sqrt[3]{327},\sqrt[3]{3343},4\sqrt{5},\sqrt{96}$ in ascending order.

1. $\sqrt[3]{327}<\sqrt[3]{3343}<4\sqrt{5}<\sqrt{96}$
2. $\sqrt[3]{327}>\sqrt[3]{3343}>4\sqrt{5}>\sqrt{96}$
3. $\sqrt[3]{3343}>\sqrt{96}>\sqrt[3]{327}>4\sqrt{5}$
4. $\sqrt[3]{3343}<\sqrt{96}<4\sqrt[3]{35}<\sqrt{27}$

Q. Compare the given numbers by comparing their approximate values: $2\sqrt{3},\sqrt{10}$

1. $2\sqrt{3}<\sqrt{10}$
2. $2\sqrt{3}>\sqrt{10}$
3. It cannot be determined as there is no common term.