show that each of the following number is a perfect square.Also find the number whose square is the given number. i) 1296 ii) 1784 iii) 3025 iv) 3969
Answers
Step-by-step explanation:
i) We know that
It can be written as
1296=2×2×2×2×3×3×3×3
Here
After pairing the same prime factors, no factor is left
Therefore, 1296 is a perfect square of 2×2×3×3×=36
ii) It can be written as
1764 = 2 × 2 × 3 × 3 × 7 × 7
Here
After pairing the same factors, no factor is left.
Therefore, 1764 is a perfect square of 2 × 3 × 7 = 42.
iii) It can be written as
3025 = 5 × 5 × 11 × 11
Here
After pairing the same prime factors, no factor is left.
Therefore, 3025 is a perfect square of 5 × 11 = 55.
iv) It can be written as
3969 = 3 × 3 × 3 × 3 × 7 × 7
Here
After pairing the same prime factors, no factor is left.
Therefore, 3969 is a perfect square of 3 × 3 × 7 = 63.
Answer:
i) We know that
It can be written as
1296=2×2×2×2×3×3×3×3
Here
After pairing the same prime factors, no factor is left
Therefore, 1296 is a perfect square
of 2×2×3×3x=36
ii) It can be written as
1764 = 2 x 2 x 3 x 3 x 7 x 7
Here
After pairing the same factors, no factor is
left.
Therefore, 1764 is a perfect square of 2 × 3 ×
7 = 42.
iii) It can be written as
3025 = 5 x 5 × 11 × 11
Here
After pairing the same prime factors, no factor is left.
Therefore, 3025 is a perfect square of 5 × 11 = 55.
iv) It can be written as 3969 = 3 x 3 x 3 x 3 x 7 x 7
Here
After pairing the same prime factors, no factor is left.
Therefore, 3969 is a perfect square of 3 × 3 x 7 = 63.