Question
Rewrite √45 in as a product of an integer and irrational square root.
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GPT 3.5
To rewrite the square root of 45 as a product of an integer and an irrational square root, we need to find the largest perfect square factor of 45. The largest perfect square factor of 45 is 9 (which is equal to 3 squared).
So, we can rewrite √45 as √(9×5).
Using the property of square roots, we can split the square root of a product into the product of the square roots:
√(9×5) = √9 × √5
Now we simplify:
√9 is equal to 3 (since 3×3 = 9), so we can rewrite √45 as 3√5.
Therefore, √45 is written as a product of an integer and an irrational square root: 3√5.
So, we can rewrite √45 as √(9×5).
Using the property of square roots, we can split the square root of a product into the product of the square roots:
√(9×5) = √9 × √5
Now we simplify:
√9 is equal to 3 (since 3×3 = 9), so we can rewrite √45 as 3√5.
Therefore, √45 is written as a product of an integer and an irrational square root: 3√5.
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