Question

just please help 6 through 8 thank you please help me its a homework but i really dont get it that much please help me​

Answer 1

Problem 6

It's not clear what the instructions are, but I'm assuming your teacher wants you to rationalize the denominator.

If so, then we could have these steps

`\sqrt{\frac{3\text{x}}{7}}\\\\\frac{\sqrt{3\text{x}}}{√(7)}\\\\\frac{\sqrt{3\text{x}}*√(7)}{√(7)*√(7)}\\\\\frac{\sqrt{3\text{x}*7}}{(√(7))^2}\\\\\frac{\sqrt{21\text{x}}}{7}\\\\`

In the third step, I multiplied top and bottom by
`√(7)` so that the denominator can get rid of the square root.

Answer:
`\frac{\sqrt{21\text{x}}}{7}\\\\`

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Problem 7

We'll follow the same idea for this problem.

`\sqrt{(5m^2)/(2)}\\\\(√(5m^2))/(√(2))\\\\(√(5m^2)*√(2))/(√(2)*√(2))\\\\(√(5m^2*2))/((√(2))^2)\\\\(√(10m^2))/(2)\\\\(√(10)*√(m^2))/(2)\\\\(m√(10))/(2)\\\\`

Where m is nonnegative.

In the second to last step, I split up the root so I could use the rule
`√(x^2) = x \text{ when } x \ge 0`

Answer:
`(m√(10))/(2)\\\\`

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Problem 8

`\sqrt{\frac{12\text{x}^3}{5}}\\\\\frac{\sqrt{12\text{x}^3}}{√(5)}\\\\\frac{\sqrt{12\text{x}^3}*√(5)}{√(5)*√(5)}\\\\\frac{\sqrt{12\text{x}^3*5}}{(√(5))^2}\\\\\frac{\sqrt{60\text{x}^3}}{5}\\\\\frac{\sqrt{4\text{x}^2*15\text{x}}}{5}\\\\\frac{\sqrt{4\text{x}^2}*\sqrt{15\text{x}}}{5}\\\\\frac{\sqrt{(2\text{x})^2}*\sqrt{15\text{x}}}{5}\\\\\frac{2x\sqrt{15\text{x}}}{5}\\\\`

where x is nonnegative.

Answer:
`\frac{2x\sqrt{15\text{x}}}{5}\\\\`