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

Multiply. Write your answer in simplest form.
√14 ⋅ √21
Transcript text: Multiply. Write your answer in simplest form. \[ \sqrt{14} \cdot \sqrt{21} \]
failed

Solution

failed
failed

Solution Steps

Step 1: Use the Property of Square Roots

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

1421=1421 \sqrt{14} \cdot \sqrt{21} = \sqrt{14 \cdot 21}

Step 2: Multiply the Numbers Inside the Square Root

Calculate the product of the numbers inside the square root.

1421=294 14 \cdot 21 = 294

Step 3: Simplify the Square Root

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

Prime factorization of 294: 294=2×3×7×7294 = 2 \times 3 \times 7 \times 7.

Since 7×7=497 \times 7 = 49 is a perfect square, we can simplify:

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

Thus, the expression simplifies to:

76 7\sqrt{6}

Final Answer

76\boxed{7\sqrt{6}}

Was this solution helpful?
failed
Unhelpful
failed
Helpful