Question

How do I find the value of the squareroot of 10 between 2 numbers?

Answer 1

The square root of 10 is between 3 and 3.5;

`\text{The value of }\sqrt[]{10}\text{ is between 3 and 3.5}`

Step-by-step explanation:

We want to find the interval in which the root of 10 falls within.

The root of 9 is 3 and the root of 16 is 4;

`\begin{gathered} \sqrt[]{9}=3 \\ \sqrt[]{16}=4 \end{gathered}`

10 is between 9 and 16, so the root of 10 is between 3 and 4;

Since the square of 3.5 is 12.25 which is also greater than 10;

`\begin{gathered} 3.5^2=12.25 \\ \text{ since;} \\ 9<10<12.25 \\ \text{then;} \\ \sqrt[]{9}<\sqrt[]{10}<\sqrt[]{12.25} \\ \text{Therefore;} \\ 3<\sqrt[]{10}<3.5 \end{gathered}`

Therefore, the square root of 10 is between 3 and 3.5;

`\text{The value of }\sqrt[]{10}\text{ is between 3 and 3.5}`