Question

(a) 1.280
(b) 405
(C) 363
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) 6,336
(b) 1.875
(c) 1,02,487
(d) 7,605​

Answer 1

Answer:

7.

(a) 6336

Solution:-

6336=(2×2)×(2×2)×(2×2)×(3×3)×(11)

We notice that all the other numbers are in pair ,i.e. 2 and 3,expect for 11.

Now,

6336÷11=576

Therefore,the smallest number that must be divided by 6336 in order to make it a perfect square,i.e. 576,is 11.

576=(2×2)×(2×2)×(2×2)×(3×3)

=2×2×2×3

=24

Therefore,the square root of 576 is 24.

(b)1875

Solution:-

1875=(5×5)×(5×5)×3

We notice that all the other number(s) are in pair,i.e. 5, except for 3.

Now,

1875÷3=625

Therefore,the smallest number that must be divided by 1875 in order to make it a perfect square,i.e. 625,is 3.

625=(5×5)×(5×5)

=5×5

=25

Therefore,the square root of 625 is 25.

(c)102487

Solution:-

102487=(11×11)(11×11)×7

We notice that all the other number(s) are in pairs, i.e. 11, except for 7.

Now,

102487÷7=14641

Therefore,the smallest number that must be divided by 102487 in order to make it a perfect square,i.e 14647,is 7.

14641=(11×11)×(11×11)

=11×11

=121

Therefore,the square root of 14641 is 121.

(d)7605

Solution:-

7605=(13×13)×(3×3)×5

We notice that all the other numbers are in pairs,i.e. 13 and 3,except for 5.

Now,

7605÷5=1521

Therefore, the smallest number that must be divided by 7605 in order to make it a perfect square,i.e. 1521,is 5.

1521=(13×13)(3×3)

=13×3

=39

Therefore, the square root of 1521 is 39.

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