Question

Using rational approximations, what is an inequality statement comparing √64 and √59.
The inequality is: v64 ____ √59

Answer 1

put that in simplier terms por favorrrr

Answer 2

To compare \( \sqrt{64} \) and \( \sqrt{59} \), we first calculate \( \sqrt{64} \):

\[
\sqrt{64} = 8
\]

Next, we need to determine \( \sqrt{59} \). We know that \( 59 \) is between \( 49 \) and \( 64 \), which means:

\[
\sqrt{49} < \sqrt{59} < \sqrt{64}
\]
\[
7 < \sqrt{59} < 8
\]

This confirms that \( \sqrt{59} \) is less than \( 8 \). We can further refine our approximation by testing squares of numbers between \( 7 \) and \( 8 \).

Let's check \( 7.5 \):

\[
7.5^2 = 56.25
\]

Now check \( 7.6 \):

\[
7.6^2 = 57.76
\]

And check \( 7.7 \):

\[
7.7^2 = 59.29
\]

Since \( 58 < 59 < 59.29 \), we have:

\[
7.6 < \sqrt{59} < 7.7
\]

This approximation confirms that \( \sqrt{59} \) is greater than \( 7.6 \) but less than \( 7.7 \).

Thus, we can conclude:

\[
\sqrt{64} > \sqrt{59}
\]

The inequality statement can be written as:

\[
\sqrt{64} > \sqrt{59}
\]

Thus, we fill in the blank to say:

\[
\sqrt{64} > \sqrt{59}
\]

Answer 3

Sure! Here’s the comparison in simpler terms:

\[
\sqrt{64} > \sqrt{59}
\]

In words: "The square root of 64 is greater than the square root of 59."

So, you can fill in the blank like this:

\[
\sqrt{64} > \sqrt{59}
\]