Question

Simplify. Assume y and x are greater than zero,
`\sqrt{49 {y}^(9){x}^(7) } / 4`

Answer 1

The simplification will give;

`\frac{7\sqrt[]{q^9r^7}}{2}`

Here, we want to make a simplification

We proceed as follows;

`\sqrt[]{(49q^9r^7)/(4)}\text{ = }\frac{\sqrt[]{49}\text{ }*\sqrt[]{q^9\text{ }}\text{ }*\sqrt[]{r^7}}{\sqrt[]{4}}`

As we can see, the power of 9 and 7 are not perfect squares since they are odd

Thus, we have the expression as;

`\frac{7*\sqrt[]{q^{9\text{ }}}\text{ }*\sqrt[]{r^7}}{2}\text{ = }\frac{7\sqrt[]{q^9r^7}}{2}`

According to laws of indices;

`\begin{gathered} a^9=a^(4.5)* a^(4.5) \\ a^6=a^3* a^3 \\ (a^9)^{(1)/(2)}=a^{(9)/(2)} \\ (a^6)^{(1)/(2)}=a^{(6)/(2)}=a^3 \end{gathered}`