Question

represent root 105 on the number line and justify your answer

Answer 1

extent it to root 105
hope you will get

Answer 2

The point to be marked on the number line is 10.24.

Given: $\sqrt{105}$

To find: Plot $\sqrt{105}$ on number line

Step by step explanation:

Basic concept used: - We will use estimation method

Step 1: The number 105 lies between the squares 100 and 121
i.e., 100 < 105 < 121
Step 2: Finding the roots of the above
⇒ $\sqrt{100} < \sqrt{105} < \sqrt{121}$
⇒ 10 < $\sqrt{105}$ < 11
Step 3: Dividing the number 105 by either 10 or 11,
∴ 105/10 = 10.5
Step 4: taking average of 10 and 10.5
∴ (10 + 10.5) / 2 = 10.25
Now, $10.25^{2}$ ≈ 105.06.
Step 5: Dividing 105.06 by 10.25
105.06/10.25 ≈ 10.24
Step 6: Taking average of 10.24 and 10.25
(10.24 + 10.25) / 2 ≈ 10.24.

∴ The square root of 105 is roughly equals to 10.24.
Now we can mark this on the number line.

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