Question

For which value of x must the expression √97x be further simplified?

5
10
15
20

Answer 1

`\bf √(97x)\qquad x=20\implies √(97\cdot 20)\qquad \begin{cases} 20\implies 2\cdot 2\cdot 5\\ \qquad 2^2\cdot 5 \end{cases} \\\\\\ √(97\cdot 2^2\cdot 5)\implies 2√(97\cdot 5)\implies 2√(485)`

Answer 2

Answer with explanation:

The Expression which is equal to ,

`=√(97 x)`

in which 97 is Prime Number, and x is a Variable.

So, for further Simplification, x must be a Composite Number, having two Identical Factor.

For, x=5,
`=√(97 x)` , can not further Simplified.

For, x=10,
`=√(97 x)` , also can not further Simplified.

For, x=15,
`=√(97 x)` , can not be further Simplified.

But for, x=20

`=√(97 * 20)\\\\=√(97 * 2* 2 * 5)\\\\=2 √(97 * 5)\\\\=2√(485)`

The Expression can be further Simplified.

Option D: 20