Which product yields an irrational number? sqrt(9) * 3; 7/8 * sqrt(25); 2sqrt(64) * 7sqrt(81); 4sqrt(5) * 2sqrt(49)

Answer 1

To determine which product yields an irrational number, we can evaluate each expression one by one.

1. \(\sqrt{9} \times 3\): \[ \sqrt{9} = 3 \quad \text{so} \quad \sqrt{9} \times 3 = 3 \times 3 = 9 \quad \text{(rational)} \]

2. \(\frac{7}{8} \times \sqrt{25}\): \[ \sqrt{25} = 5 \quad \text{so} \quad \frac{7}{8} \times \sqrt{25} = \frac{7}{8} \times 5 = \frac{35}{8} \quad \text{(rational)} \]

3. \(2\sqrt{64} \times 7\sqrt{81}\): \[ \sqrt{64} = 8 \quad \text{and} \quad \sqrt{81} = 9 \] \[ 2\sqrt{64} \times 7\sqrt{81} = 2 \times 8 \times 7 \times 9 = 2 \times 56 \times 9 = 112 \times 9 = 1008 \quad \text{(rational)} \]

4. \(4\sqrt{5} \times 2\sqrt{49}\): \[ \sqrt{49} = 7 \quad \text{so} \quad 4\sqrt{5} \times 2\sqrt{49} = 4\sqrt{5} \times 2 \times 7 = 8 \times 7\sqrt{5} = 56\sqrt{5} \quad \text{(irrational)} \]

Therefore, the product that yields an irrational number is:

\(4\sqrt{5} \times 2\sqrt{49}\).