Arrange the following numbers in ascending or | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) To compare the numbers $\sqrt{3}, \sqrt[3]{4}, \sqrt[4]{10}$,we express them as powers with a common index.$1$. The indices are $2, 3, 4$. The lea

Vedclass · Accepted Answer

$\sqrt[3]{4} < \sqrt{3} < \sqrt[4]{10}$

Vedclass · Answer

(B) To compare the numbers $\sqrt{3}, \sqrt[3]{4}, \sqrt[4]{10}$,we express them as powers with a common index.$1$. The indices are $2, 3, 4$. The least common multiple $(LCM)$ of $2, 3, 4$ is $12$.$2$. Convert each number to the $12^{th}$ root:$\sqrt{3} = 3^{1/2} = 3^{6/12} = \sqrt[12]{3^6} = \sqrt[12]{729}$$\sqrt[3]{4} = 4^{1/3} = 4^{4/12} = \sqrt[12]{4^4} = \sqrt[12]{256}$$\sqrt[4]{10} = 10^{1/4} = 10^{3/12} = \sqrt[12]{10^3} = \sqrt[12]{1000}$$3$. Comparing the values inside the $12^{th}$ root: $256 $4$. Therefore,the ascending order is $\sqrt[12]{256} < \sqrt[12]{729} < \sqrt[12]{1000}$,which corresponds to $\sqrt[3]{4} < \sqrt{3} < \sqrt[4]{10}$.

Arrange the following numbers in ascending order: $\sqrt{3}, \sqrt[3]{4}, \sqrt[4]{10}$

Similar Questions

Express the following in the form $\frac{p}{q},$ where $p$ and $q$ are integers and $q \neq 0$ :
$0 . \overline{001}$

Locate $\sqrt{5}, \sqrt{10}$ and $\sqrt{17}$ on the number line.

Simplify: $\frac{8^{\frac{1}{3}} \times 16^{\frac{1}{3}}}{32^{-\frac{1}{3}}}$

Convert the following rational number into decimal form and state the kind of its decimal expansion:
$\frac{4}{13}$

Represent $\sqrt{8.1}$ geometrically on the number line.

Vedclass Test Series

Exam Paper Generator

Online Exam Module