Question

7. Find the smallest numbers by which the following numbers should be divided so as to get perfect squares.
Also find the square roots of the numbers so obtained:
(a)7,605​

Answer 1

Answer:

7605 = 5*3*3*13*13

here 3 and 13 have their pairs but 5 don't have

so, the no. should be divided by 5 to get perfect square .

the no. is 1521 ; √1521 = 39

Answer 2

Step-by-step explanation:

By prime factorisation, we get

252=

2×2

×

3×3

×7

Since the prime factor 7 cannot be paired.

∴ The given number should be divided by

∴

7

252

=

7

2×2×3×3×7

2∣252

2∣126

3∣63

3∣21

7∣7

∣1

=

2×2

×

3×3

=36 is a perfect square.

and,

36

=

2×2

×

3×3

=2×3=6

By prime factorisation, we get

2925=

3×3

×

5×5

×13

Since prime factor 13 cannot be paired.

∴ The given number should be divided by 13.

∴

13

2925

=

13

3×3×5×5×13

3∣2925

3∣975

5∣325

5∣65

13∣13

∣1

=

3×3

×

5×5

=225 is a perfect square

and,

225

=

3×3

×

5×5

=3×5=15.