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