Question

find the smallest number by which 3125 be divided to get a perfect square

a)4
b)5
c)10
d)none of these​

Answer 1

Answer:

I should be divided by 5

Step-by-step explanation:

3125/5=625

625 is the square of 25

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Answer 2

The smallest number by which 3125 be divided to get a perfect square is 5.

Option (b) is correct.

Given:

• 3125

To find:

• find the smallest number by which 3125 be divided to get a perfect square

• a)4
• b)5
• c)10
• d)none of these

Solution:

Concept to be used:

We know that $\bf \sqrt{ {a}^{2n} } = {a}^{n}$

Step 1:

Write the prime factors of 3125.

$3125 = 5 \times 5 \times 5 \times 5 \times 5$

or

$3125 = {3}^{5}$

Step 2:

It is clear that 5 is not a multiple of 2.

Thus,

To convert the power of 5 as multiple of 2, we have to divide it by 5.

So,

$\frac{3125}{5} = \frac{ {5}^{5} }{5}$

or

$625 = {5}^{4}$

or

$625 = {5}^{2 \times 2}$

on comparison with the formula;

$\sqrt{625} = \sqrt{ {5}^{(2 \times 2)} } = {5}^{2}$

or

$\bf \sqrt{625} = 25$

Thus,

The smallest number by which 3125 be divided to get a perfect square is 5.

Option (b) is correct.

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