Question

Without plotting these numbers, decide which inequalities are true. Check all that apply. StartRoot 7 EndRoot > 2 StartRoot 7 EndRoot < 7 StartRoot 7 EndRoot < StartRoot 8 EndRoot StartRoot 8 EndRoot < 2 StartRoot 8 EndRoot < 8

Answer 1

Answer:

$\sqrt7> 2$

$\sqrt7< 7$

$\sqrt7< \sqrt8$

$\sqrt8< 8$

are true.

Step-by-step explanation:

Given inequalities are:

$\sqrt7> 2$

$\sqrt7< 7$

$\sqrt7< \sqrt8$

$\sqrt8< 2$

$\sqrt8< 8$

To find:

Without plotting these numbers, decide Which of the inequalities are true?

Solution:

Let us consider them one by one:

$\sqrt7$ can be written as : $\sqrt{4+3}$

Value of $\sqrt4$ is equal to 2 (which is the Right hand side of the inequality)

Therefore, $\bold{\sqrt7>2}$ is true.

$\sqrt7< 7$

Its RHS can be written as: $\sqrt7 \times \sqrt7$

In RHS, LHS is multiplied by LHS itself.

And when a number greater than 1 is multiplied with itself, its value increases.

Therefore, $\bold{\sqrt7< 7}$ is true.

$\sqrt7< \sqrt8$

7 < 8 so its root will also follow the same.

$\therefore \bold{\sqrt7< \sqrt8}$ is also true.

$\sqrt8< 2$

Left Hand Side (LHS) can be written as:

$\sqrt8 = \sqrt{2 \times 2 \times 2} =2\sqrt2$

and $\sqrt2 > 1$ Hence, multiplying 2 with a number greater than 1 will make it greater than 2.

That means $2\sqrt2>2$

Therefore, the given inequality $\sqrt8< 2$is false.

$\sqrt8< 8$

Its RHS can be written as: $\sqrt8 \times \sqrt8$

In RHS, LHS is multiplied by LHS itself.

And when a number greater than 1 is multiplied with itself, its value increases.

Therefore, $\sqrt8< 8$ is true.