Which is bigger, `(10)/(7)or ((10)/(7))^(2)`?

Answer

To determine which is bigger between \(\frac{10}{7}\) and \(\left(\frac{10}{7}\right)^2\), we can follow these steps:

### Step 1: Calculate \(\left(\frac{10}{7}\right)^2\)
To find \(\left(\frac{10}{7}\right)^2\), we square both the numerator and the denominator:
\[ \left(\frac{10}{7}\right)^2 = \frac{10^2}{7^2} = \frac{100}{49} \]

### Step 2: Compare \(\frac{10}{7}\) and \(\frac{100}{49}\)
Now we need to compare \(\frac{10}{7}\) and \(\frac{100}{49}\). To do this, we can cross-multiply to avoid dealing with decimals:
\[ 10 \times 49 \quad \text{and} \quad 7 \times 100 \]
Calculating both sides:
\[ 10 \times 49 = 490 \]
\[ 7 \times 100 = 700 \]

### Step 3: Determine which product is larger
Now we compare the two products:
\[ 490 \quad \text{and} \quad 700 \]
Since \(490 < 700\), we conclude that:
\[ \frac{10}{7} < \frac{100}{49} \]

### Step 4: Conclusion
Thus, we can conclude that:
\[ \left(\frac{10}{7}\right)^2 = \frac{100}{49} \text{ is greater than } \frac{10}{7} \]

### Final Answer
\(\left(\frac{10}{7}\right)^2\) is bigger than \(\frac{10}{7}\).

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