Questions: Multiply. Write your answer in simplest form. √14 ⋅ √21

Solution Steps

Use the property of square roots that states $\sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b}$.

$$\sqrt{14} \cdot \sqrt{21} = \sqrt{14 \cdot 21}$$

Calculate the product of the numbers inside the square root.

$$14 \cdot 21 = 294$$

Simplify $\sqrt{294}$ by finding the prime factorization of 294 and identifying any perfect squares.

Prime factorization of 294: $294 = 2 \times 3 \times 7 \times 7$.

Since $7 \times 7 = 49$ is a perfect square, we can simplify:

$$\sqrt{294} = \sqrt{2 \times 3 \times 49} = \sqrt{2 \times 3} \times \sqrt{49} = \sqrt{6} \times 7$$

Thus, the expression simplifies to:

$$7\sqrt{6}$$

Final Answer