Mathematics » Introducing Decimals » Simplify and Use Square Roots

Estimating Square Roots

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Estimating Square Roots

So far we have only worked with square roots of perfect squares. The square roots of other numbers are not whole numbers.

Estimating Square Roots

We might conclude that the square roots of numbers between \(4\) and \(9\) will be between \(2\) and \(3,\) and they will not be whole numbers. Based on the pattern in the table above, we could say that \(\sqrt{5}\) is between \(2\) and \(3.\) Using inequality symbols, we write

\(2<\sqrt{5}<3\)

Example

Estimate \(\sqrt{60}\) between two consecutive whole numbers.

Solution

Think of the perfect squares closest to \(60.\) Make a small table of these perfect squares and their squares roots.

Estimating Square Roots

\(\text{Locate 60 between two consecutive perfect squares.}\)\(49<60<64\)
\(\sqrt{60}\phantom{\rule{0.2em}{0ex}}\text{is between their square roots.}\)\(7<\sqrt{60}<8\)

Optional Video: Introduction to Square Roots

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