Multiply 93 −−√ ⋅67–√ . Give an exact answer.(1 point)

1 answer

To find the product \( \sqrt{93} \cdot \sqrt{67} \), we can use the property of square roots that states:

\[ \sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b}. \]

Applying this to our problem:

\[ \sqrt{93} \cdot \sqrt{67} = \sqrt{93 \cdot 67}. \]

Now we need to calculate \( 93 \cdot 67 \):

\[ 93 \cdot 67 = 93 \times 67. \]

Calculating this step-by-step:

First, we can break it down as follows:

\[ 93 \times 67 = 93 \times (60 + 7) = 93 \times 60 + 93 \times 7. \]

Calculating each part:

  • \( 93 \times 60 = 5580 \),
  • \( 93 \times 7 = 651 \).

Now, adding those results together:

\[ 5580 + 651 = 6231. \]

Thus, we have:

\[ 93 \cdot 67 = 6231. \]

Now substituting back into our square root:

\[ \sqrt{93} \cdot \sqrt{67} = \sqrt{6231}. \]

Therefore, the exact answer is:

\[ \sqrt{6231}. \]