To simplify [tex]\(\sqrt{\frac{100}{49}}\)[/tex], let's break it down step-by-step:
Step 1: We start with the expression inside the square root:
[tex]\[ \sqrt{\frac{100}{49}} \][/tex]
Step 2: We can take the square root of the numerator and the denominator separately. This is based on the property of square roots:
[tex]\[ \sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}} \][/tex]
Step 3: Calculate the square root of the numerator [tex]\(100\)[/tex]:
[tex]\[ \sqrt{100} = 10 \][/tex]
Step 4: Calculate the square root of the denominator [tex]\(49\)[/tex]:
[tex]\[ \sqrt{49} = 7 \][/tex]
Step 5: Now we can write the fraction with these simplified square roots:
[tex]\[ \frac{\sqrt{100}}{\sqrt{49}} = \frac{10}{7} \][/tex]
Therefore, the fraction simplifies to:
[tex]\[ \frac{10}{7} \][/tex]
So, we can write the simplified form of [tex]\(\sqrt{\frac{100}{49}}\)[/tex] as:
[tex]\[ \sqrt{\frac{100}{49}} = \frac{10}{7} \][/tex]
In decimal form, [tex]\(\frac{10}{7}\)[/tex] is approximately:
[tex]\[ 1.4285714285714286 \][/tex]
Thus, the simplified form of [tex]\(\sqrt{\frac{100}{49}}\)[/tex] is [tex]\(\frac{10}{7}\)[/tex] or approximately 1.4285714285714286 in decimal form.
