Sure! To solve [tex]\( -\sqrt{\frac{64}{25}} \)[/tex], let's break it down into detailed steps:
1. Understand the Problem:
We need to simplify the expression [tex]\( -\sqrt{\frac{64}{25}} \)[/tex].
2. Calculate the Square Root of the Fraction:
First, find the square root of the fraction [tex]\(\frac{64}{25}\)[/tex].
[tex]\[
\sqrt{\frac{64}{25}}
\][/tex]
3. Simplify the Fraction:
To simplify [tex]\(\sqrt{\frac{64}{25}}\)[/tex], we take the square root of the numerator and the denominator separately.
[tex]\[
\sqrt{\frac{64}{25}} = \frac{\sqrt{64}}{\sqrt{25}}
\][/tex]
4. Calculate the Square Roots Individually:
- The square root of 64 is 8.
- The square root of 25 is 5.
So, we have:
[tex]\[
\frac{\sqrt{64}}{\sqrt{25}} = \frac{8}{5}
\][/tex]
5. Simplify the Fraction:
Now, simplify [tex]\(\frac{8}{5}\)[/tex]:
[tex]\[
\frac{8}{5} = 1.6
\][/tex]
6. Apply the Negative Sign:
Finally, apply the negative sign in front of the square root:
[tex]\[
-\sqrt{\frac{64}{25}} = -1.6
\][/tex]
Therefore, the final result is:
[tex]\[
-\sqrt{\frac{64}{25}} = -1.6
\][/tex]
Intermediate and simplified results:
[tex]\[
\sqrt{\frac{64}{25}} = 1.6, \quad -\sqrt{\frac{64}{25}} = -1.6
\][/tex]
