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Estimating Square Roots

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.

A table is shown with 2 columns. The first column is labeled “Number” and contains the values: 4, 5, 6, 7, 8, 9. The second column is labeled “Square root” and contains the values: square root of 4 equals 2, square root of 5, square root of 6, square root of 7, square root of 8, square root of 9 equals 3.

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.

A table is shown with 2 columns. The first column is labeled “Number” and contains the values: 36, 49, 64, and 81. There is a balloon coming out of the table between 49 and 64 that says 60. The second column is labeled “Square root” and contains the values: 6, 7, 8, and 9. There is a balloon coming out of the table between 7 and 8 that says square root of 60.

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

Optional Video: Introduction to Square Roots

This lesson is part of:

Introducing Decimals

View Full Tutorial

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