Question

Determine if 3√10 /4 is in simplest form. if the expression is not in simplest form explain why? HELP PLEASE

Answer 1

The notation in its current form isn't entirely clear.

Did you mean to write $\frac{3\sqrt{10}}{4}$? The 4 isn't in the square root.

If so, then the expression is in simplest form because we cannot simplify $\sqrt{10}$ any further (note how 10 doesn't have any perfect square factors other than 1).

Also, the 3/4 portion is fully reduced already.

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Or,

Did you mean to write $3\sqrt{\frac{10}{4}}$ ? This time the 4 is inside the square root.

If so, then we can simplify like this

$3\sqrt{\frac{10}{4}}\\\\\frac{3\sqrt{10}}{\sqrt{4}}\\\\\frac{3\sqrt{10}}{2}$

This means that $3\sqrt{\frac{10}{4}}=\frac{3\sqrt{10}}{2}$