Question

5. Using prime factorization, find out which of the following numbers are perfect squares. Also find the
number whose square is given.
(a) 9.248 (b) 7,396 (c) 1.944 (d)
8,649 (e) 15,625 (f) 5.292 (g) 415
frontest three digit number which is a perfect square.​

Answer 1

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