Question

Between which two integers does √64 lie?

Answer 1

\(8^2=64\).

Answer 2

The definition of the square root is as follows.

Square root of x is mathematically written as \(\sqrt{x}\), and what it means is that suppose that \(x=w^2=w\cdot w \), for some \(w\), then we say \(\sqrt{x}=w\).

Answer 3

For example, we know that \(4=2^2=2\cdot 2\), therefore \(\sqrt{4}=2\).

Answer 4

Basically, to find the square root of a number (x), you ask yourself a question:
\(\rm What~number~should~I~multiply~times~itself~to~get~\)\(x?\)

Answer 5

Well, we know that \(64=8\times 8\), right?

Answer 6

So, by the same logic, square root of 64, (or \(\sqrt{64}\)) is equal to what?

Answer 7

I will assume you will be able to find this number.

Answer 8

So, I have given you the tools to find the square root of 64. Now I will do an example, similar to your problem.

Answer 9

\(\large \color{black}{{\rm Example:}}\) \(\\[0.5em]\)

\(\color{blue}{{\rm Between{\tiny~~~}which{\tiny~~~}two{\tiny~~~}integers{\tiny~~~}does}{\tiny~~~}\sqrt{36}{\tiny~~~}{\rm lie?}}\) \(\\[0.5em]\)
\(\color{blue}{{\rm You{\tiny~~~}know{\tiny~~~}that}{\tiny~~~}36=6\times 6,{\tiny~~~}{\rm thus,{\tiny~~~}}\sqrt{36}=6.}\) \(\\[0.5em]\)
\(\color{blue}{{\rm Between{\tiny~~~}which{\tiny~~~}two{\tiny~~~}integers{\tiny~~~}does}{\tiny~~~}6{\tiny~~~}{\rm lie?}}\) \(\\[0.5em]\)
\(\color{blue}{{\rm Obviously,{\tiny~~~}between{\tiny~~~}}5{\tiny~~~}{\rm and}{\tiny~~~}7.}\)