Question
Which number is equivalent to: 610−−√⋅39–√610⋅39 ?(1 point) Responses 990−−√9909 square root of 90 919−−√9199 square root of 19 5410−−√541054 square root of 10 1809–√
Answers
GPT-4o mini
To solve the expression \( \sqrt{610} \cdot \sqrt{39} \div \sqrt{610 \cdot 39} \), we can use the property of square roots that states \( \sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b} \).
So first, we simplify the expression:
\[
\sqrt{610} \cdot \sqrt{39} = \sqrt{610 \cdot 39}
\]
Thus,
\[
\sqrt{610} \cdot \sqrt{39} \div \sqrt{610 \cdot 39} = \frac{\sqrt{610 \cdot 39}}{\sqrt{610 \cdot 39}} = 1
\]
Therefore, the final equivalent number for the original expression is \( 1 \).
However, looking closely at the response options provided, this number is not included in the options given. It seems there may be an understanding issue if \( 1 \) is not an available option. Please clarify if any other instructions or options are presented or could you share the response options again?
So first, we simplify the expression:
\[
\sqrt{610} \cdot \sqrt{39} = \sqrt{610 \cdot 39}
\]
Thus,
\[
\sqrt{610} \cdot \sqrt{39} \div \sqrt{610 \cdot 39} = \frac{\sqrt{610 \cdot 39}}{\sqrt{610 \cdot 39}} = 1
\]
Therefore, the final equivalent number for the original expression is \( 1 \).
However, looking closely at the response options provided, this number is not included in the options given. It seems there may be an understanding issue if \( 1 \) is not an available option. Please clarify if any other instructions or options are presented or could you share the response options again?