Question

Which two perfect squares should be used to estimate sqrt(95)

Answer 1

81 and 100

Step-by-step explanation

We have to determine two numbers around 95 - one greater than 95 and another less than 95 - whose square roots give whole numbers (these are called perfect squares).

We know that 100 is the result of 10², therefore it's a perfect square. Before selecting it as the greater number, we have to see if there's a lower value that's above 95 and is a perfect square. The next perfect square less than 10² is 9² = 81. Therefore we have the two perfect squares for which 95 is in the middle: 81 and 100.

This way, we can estimate that √95 is between 9 and 10. In other words:

`\begin{gathered} \sqrt[]{81}\lt\sqrt[]{95}\lt\sqrt[]{100} \\ 9\lt\sqrt[]{95}\lt10 \end{gathered}`