the perfect square number between 441 and 529
Answers
Answer:
method, find which of the following numbers are perfect squares:
(i) 441
(ii) 576
(iii) 11025
(iv) 1176
(v) 5625
(vi) 9075
(vii) 4225
(viii) 1089
ANSWER:
A perfect square can always be expressed as a product of equal factors.
(i)
Resolving into prime factors:
441=49×9=7×7×3×3=7×3×7×3=21×21=(21)2
Thus, 441 is a perfect square.
(ii)
Resolving into prime factors:
576=64×9=8×8×3×3=2×2×2×2×2×2×3×3=24×24=(24)2
Thus, 576 is a perfect square.
(iii)
Resolving into prime factors:
11025=441×25=49×9×5×5=7×7×3×3×5×5=7×5×3×7×5×3=105×105=(105)2
Thus, 11025 is a perfect square.
(iv)
Resolving into prime factors:
1176=7×168=7×21×8=7×7×3×2×2×2
1176 cannot be expressed as a product of two equal numbers. Thus, 1176 is not a perfect square.
(v)
Resolving into prime factors:
5625=225×25=9×25×25=3×3×5×5×5×5=3×5×5×3×5×5=75×75=(75)2
Thus, 5625 is a perfect square.
(vi)
Resolving into prime factors:
9075=25×363=5×5×3×11×11=55×55×3
9075 is not a product of two equal numbers. Thus, 9075 is not a perfect square.
(vii)
Resolving into prime factors:
4225=25×169=5×5×13×13=5×13×5×13=65×65=(65)2
Thus, 4225 is a perfect square.
(viii)
Resolving into prime factors:
1089=9×121=3×3×11×11=3×11×3×11=33×33=(33)2
Thus, 1089 is a perfect square.
Step-by-step explanation:
C) 441, 529, 676, 841
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