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secondary 2 | Maths
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need help ASAP !!! detail explanation please !! thank uuu
Date Posted: 2 years ago
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Perfect square means the number is a product of two identical whole numbers.
Eg. 0 = 0 × 0 = 0², 4 = 2 × 2 = 2², 81 = 9 × 9 = 9²
For 27y to be a perfect square, you need the powers of its prime factors to be even so they can be rewritten as the square of some other number or power.
Idea here is to break 27 down into its prime factors first.
27 = 3 × 3 × 3 = 3³
So, 27y = 3 × 3 × 3 × y
We see three copies of '3' . We need a minimum of one more to make the power even. So y must contain a prime factor '3'
Turns out that is all we need.
When y = 3, 27y
= 3³ × 3
= 3⁴
= (3 × 3) × (3 × 3)
= 3² × 3²
= 9 × 9
= 9² (a perfect square)
(Note that 3⁴ can be rewritten immediately as (3²)² = 9². You will learn more of indices at Sec 3)
So smallest y = 3
Eg. 0 = 0 × 0 = 0², 4 = 2 × 2 = 2², 81 = 9 × 9 = 9²
For 27y to be a perfect square, you need the powers of its prime factors to be even so they can be rewritten as the square of some other number or power.
Idea here is to break 27 down into its prime factors first.
27 = 3 × 3 × 3 = 3³
So, 27y = 3 × 3 × 3 × y
We see three copies of '3' . We need a minimum of one more to make the power even. So y must contain a prime factor '3'
Turns out that is all we need.
When y = 3, 27y
= 3³ × 3
= 3⁴
= (3 × 3) × (3 × 3)
= 3² × 3²
= 9 × 9
= 9² (a perfect square)
(Note that 3⁴ can be rewritten immediately as (3²)² = 9². You will learn more of indices at Sec 3)
So smallest y = 3
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