Question

mace
6. Find the smallest number by which each of the following numbers should be multiplied to get perfect
squares:
(a) 1,280
(b) 405
(c) 363
(d) 3.564​

Answer 1

Answer:

(a) we must multiply 5 with 1280 to get a perfect square.

(b) 5 must be multiplied with 405 to make it a perfect square.

(c) 3 must be multiplied with 363 to get a perfect square.

(d) 11 must be multiplied with 3564 to get a perfect square.

Step-by-step explanation:

We must know that,

For a number to be a perfect square, its prime factorization must have factors in pairs.

For example

100 = 2 × 2 × 5 × 5 = 2² × 52²

We see that, 2 and 5 are in pairs

Hence, 100 is a perfect square.

√100 = 10

Now, back to our Original problem.

(a) 1280

1280 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 5

1280 = 2² × 2² × 2² × 2² × 5

Here 5 is not in pair, thus making 1280 a non perfect square, So to make it a perfect square we multiple 5.

1280 × 5 = 6400

√6400 = 80

Thus, we must multiply 5 with 1280 to get a perfect square.

(b) 405

405 = 3 × 3 × 3 × 3 × 5

405 = 3² × 3² × 5

Here also 5 is not in pair,

So, 5 must be multiplied with 405 to make it a perfect square.

(c) 363

363 = 3 × 11 × 11

363 = 3 × 11²

Here 3 is not in pairs,

So, 3 must be multiplied with 363 to get a perfect square.

(d) 3564

3564 = 2 × 2 × 3 × 3 × 3 × 3 × 11

3564 = 2² × 3² × 3² × 11

Here 11 is not in pairs,

So, 11 must be multiplied with 3564 to get a perfect square.

Hope it helped and believing you understood it........All the best

Answer 2

Answer:

(a) 5

(b) 5

(c) 3

(d) 11

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