Question

The smallest positive natural number n for which 125 x n is a perfect
square is​

Answer 1

Answer:

ANSWER

125×n

125=5³

yes! it is perfect square

Step-by-step explanation:

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Answer 2

Answer:

Required value of n is 5.

Step-by-step explanation:

Here given term is $125 \times n$

We want to find the smallest positive natural number n for which 125 x n is a perfect square.

This is a problem of power of indices.

For find the answer,first we need to break 125 into prime numbers.

So,$125 = 5 \times 5 \times 5$

Here 125 means power is 3 of 5.

Power of 5 is odd.We need to convert it into even number.

It is clear that if we multiplied 125 by 5 then 125x5 becomes perfect square.

So value of n is 5 where 5 is a natural number.

Some formulas of power of indices,

${x}^{0} = 1 \\ {x}^{1} = x \\ {x}^{a} \times {x}^{b} = {x}^{a + b} \\ \frac{ {x}^{a} }{ {x}^{b} } = {x}^{a - b} \\ {x}^{ {y}^{a} } = {x}^{ya} \\ {x}^{ - 1} = \frac{1}{x} \\ {x}^{a} \times {y}^{a} = {(xy)}^{a}$