Question

show that each of the following numbers is a perfect square . in each case , find the number whose square is the given number


1 1225
2 5926
3 8281​

Answer 1

Step-by-step explanation:

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)