Question

Give reasons that 300 lies between 17 and 18.​

Answer 1

Answer:

300 pies between 17 and 18 because 299 comes before 300 and 301 comes after 300 so by this we can say 300lies between 17 and 18

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Answer 2

Correct Question: Give reasons that $\sqrt{300}$ lies between 17 and 18.​

Answer:

17 < $\sqrt{300}$ < 18,  $\sqrt{300}$ lies between 17 and 18.​

Step-by-step explanation:

Consider the number as follows:

$\sqrt{300}$

Since $\sqrt{300}$ is an irrational number, i.e., it cannot be written in p/q form.

In other words, irrational numbers are non-terminating and non-repeating decimals.

So, the value of $\sqrt{300}$ is 17.3205080......

⇒ $\sqrt{300} = 17.32$ (approximately)

Observe that,

17.32 = 17 + 0.32

⇒ 17.32 > 17 ...... (i)

Also, 18 > 17.32 ...... (ii)

Form (i) and (ii), we get

⇒ 17 < 17.32 < 18

⇒ 17 < $\sqrt{300}$ < 18

Thus, the number $\sqrt{300}$ lies between 17 and 18.​

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