To simplify the expression
[tex]\[
\sqrt{\frac{16}{49}}
,
\][/tex]
we can follow these steps:
1. Recognize that the square root of a fraction is the same as the fraction of the square roots of the numerator and the denominator. This property is expressed mathematically as:
[tex]\[
\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}
\][/tex]
2. Identify the numerator and the denominator of the given fraction. Here, we have:
[tex]\[
\frac{16}{49}
\][/tex]
3. Find the square root of the numerator. The numerator is 16, and the square root of 16 is:
[tex]\[
\sqrt{16} = 4
\][/tex]
4. Find the square root of the denominator. The denominator is 49, and the square root of 49 is:
[tex]\[
\sqrt{49} = 7
\][/tex]
5. Combine these results to form the simplified fraction:
[tex]\[
\frac{\sqrt{16}}{\sqrt{49}} = \frac{4}{7}
\][/tex]
6. Lastly, we can conclude that the original expression simplifies to:
[tex]\[
\sqrt{\frac{16}{49}} = \frac{4}{7} \approx 0.5714285714285714
\][/tex]
By breaking down the problem into these steps, we see that the simplified form of
[tex]\[
\sqrt{\frac{16}{49}}
\][/tex]
is
[tex]\[
\frac{4}{7}
.
\][/tex]
