To rewrite the irrational square root \( \sqrt{72} \) as the product of an integer and another irrational square root, we can first simplify \( \sqrt{72} \).
Start by factoring 72: \[ 72 = 36 \times 2 \]
Now, we can use this factorization to simplify \( \sqrt{72} \): \[ \sqrt{72} = \sqrt{36 \times 2} \] Using the property of square roots that states \( \sqrt{a \times b} = \sqrt{a} \times \sqrt{b} \), we can write: \[ \sqrt{72} = \sqrt{36} \times \sqrt{2} \]
Since \( \sqrt{36} = 6 \), we have: \[ \sqrt{72} = 6 \times \sqrt{2} \]
Thus, the irrational square root \( \sqrt{72} \) can be rewritten as: \[ \sqrt{72} = 6 \sqrt{2} \]
So the answer is: \[ 6 \sqrt{2} \]
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