To simplify the expression [tex]\(\sqrt{\frac{16}{25}}\)[/tex], let's follow these steps:
### Step 1: Express the square root of the fraction as a fraction of square roots
The square root of a fraction can be written as the fraction of the square roots of the numerator and the denominator:
[tex]\[
\sqrt{\frac{16}{25}} = \frac{\sqrt{16}}{\sqrt{25}}
\][/tex]
### Step 2: Simplify the square root of the numerator
Next, simplify [tex]\(\sqrt{16}\)[/tex]:
[tex]\[
\sqrt{16} = 4
\][/tex]
### Step 3: Simplify the square root of the denominator
Now, simplify [tex]\(\sqrt{25}\)[/tex]:
[tex]\[
\sqrt{25} = 5
\][/tex]
### Step 4: Write the simplified form of the fraction
Putting the simplified numerator and denominator together, we get:
[tex]\[
\frac{\sqrt{16}}{\sqrt{25}} = \frac{4}{5}
\][/tex]
### Step 5: Recalculate the fraction if needed
There is no further simplification needed since [tex]\( \frac{4}{5} \)[/tex] is already in its simplest form.
### Conclusion
The simplified form of the expression [tex]\(\sqrt{\frac{16}{25}}\)[/tex] is:
[tex]\[
\frac{4}{5}
\][/tex]
Thus, [tex]\(\sqrt{\frac{16}{25}} = \frac{4}{5}\)[/tex], and since [tex]\(\frac{4}{5} = 0.8\)[/tex]:
\boxed{\frac{4}{5}, 0.8}
