Question

Arrange the surds in descending order: 3√5,9√4,6√3​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

The required descending order is: 9√4, 6√3​, 3√5.

Step-by-step explanation:

Consider the provided information.

3√5, 9√4, 6√3​

We need to arrange them in descending order.

Remember:

3 can be written as: $\sqrt{3\times 3} =\sqrt{9}$

Similarly, 9 can be written as: $\sqrt{9\times 9} =\sqrt{81}$

Similarly, 6 can be written as: $\sqrt{6\times 6} =\sqrt{36}$

Now, rewrite the numbers as shown below:

$3\sqrt{5} = \sqrt{9} \times \sqrt{5}=\sqrt{45}$

$9\sqrt{4} = \sqrt{81} \times \sqrt{4}=\sqrt{324}$

$6\sqrt{3} = \sqrt{36} \times \sqrt{3}=\sqrt{108}$

Now by the comparison we can concluded that, $\sqrt{324}$ is the largest number, and $\sqrt{45}$ is the smallest number.

Now arrange them in descending order.

$\sqrt{324}>\sqrt{108}>\sqrt{45}$

Hence, the required descending order is: $9\sqrt{4}>6\sqrt{3}>3\sqrt{5}$.