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Answer (4)
1008 = 7 ⋅ 144 = 12 7 A n s w er i s 12 t im es s q u a re roo t o f 7
The square root of 1008 is 12√7
Now to find the square root of 1008 we would find the factors of 1008 first
Thus we get,
1008 = 2 ∗ 504 1008 = 2 ∗ 2 ∗ 252 1008 = 2 ∗ 2 ∗ 2 ∗ 126 1008 = 2 ∗ 2 ∗ 2 ∗ 2 ∗ 63 1008 = 2 ∗ 2 ∗ 2 ∗ 2 ∗ 7 ∗ 9 1008 = 4 ∗ 4 ∗ 7 ∗ 9
Now the square root of 1008 can be obtained as:
1008 = 4 ∗ 4 ∗ 7 ∗ 9 1008 = 2 ∗ 2 ∗ 3 ∗ 7 1008 = 12 7
Thus 12√7 is the required answer
To simplify the square root of 1008, we find that it factors into prime factors and can be expressed as 12 7 . This involves factoring 1008 into 2 4 × 3 2 × 7 and taking the square roots of the perfect squares out of the radical. Therefore, the final simplified answer is 12 7 .
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