Kinh Nghiệm Hướng dẫn Find the smallest number by which the given number must be multiplied to make it a perfect square Mới Nhất
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(i) 23805
Nội dung chính
- How do you find the smallest number multiplied to make a perfect square?
- How do you find the smallest number by which a number must be multiplied to obtain a perfect cube?
- What is the smallest number by which 24 must be multiplied to give a perfect square?
- Is 23805 a perfect square?
First find the prime factors for 23805
23805 = 3×3×23×23×5
By grouping the prime factors in equal pairs we get,
= (3×3) × (23×23) × 5
By observation, prime factor 5 is left out.
So, multiply by 5 we get,
23805 × 5 = (3×3) × (23×23) × (5×5)
= (3×5×23) × (3×5×23)
= 345 × 345
= (345)2
∴ Product is the square of 345.
(ii) 12150
First find the prime factors for 12150
12150 = 2×2×2×2×3×3×5×5×2
By
grouping the prime factors in equal pairs we get,
= (2×2) × (2×2) × (3×3) × (5×5) × 2
By observation, prime factor 2 is left out.
So, multiply by 2 we get,
12150 × 2 = (2×2) × (2×2) × (3×3) × (5×5) × (2×2)
= (2×2×3×5×2) × (2×2×3×5×2)
= 120 × 120
= (120)2
∴ Product is the square of 120.
(iii) 7688
First find the prime factors for 7688
7688 = 2×2×31×31×2
By grouping the prime factors in equal pairs we get,
= (2×2) ×
(31×31) × 2
By observation, prime factor 2 is left out.
So, multiply by 2 we get,
7688 × 2 = (2×2) × (31×31)× (2×2)
= (2×31×2) × (2×31×2)
= 124 × 124
= (124)2
∴ Product is the square of 124.
How do you find the smallest number multiplied to make a perfect square?
The smallest number it needs to be multiplied to make it a perfect square is 2. So for 648 to be a perfect square, the smallest number to be multiplied is 2.
How do you find the smallest number by which a number must be multiplied to obtain a perfect cube?
Hence, the smallest number by which 100 must be multiplied to obtain a perfect cube is 2×5=10.
What is the smallest number by which 24 must be multiplied to give a perfect square?
The smallest number by which 24 should be multiplied to make it a perfect square? Therefore the least number by which 24 should be multiplied is 6.
Is 23805 a perfect square?
Therefore, 5 is the smallest number by which 23805 must be multiplied so that the product is a perfect square.
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