Question

How is the number in the square root called (number 4) how can I place that in a calculator

Answer 1

The 4 in the symbol is the index of the radical sign √.

Whether you can write this expression on a calculator depends on the calculator... If you have one with a CAS (that is, a "computer algebraic system"), chances are there is a built-in button for things like square roots and cube roots, and possibly roots of higher indices. If not, you can always express a radical expression using a fractional exponent, such as

`\sqrt x\iff x^(\frac12)`

or

`\sqrt[3]{x}\iff x^(\frac13)`

or

`\sqrt[4]{x}\iff x^(\frac14)`

and so on. So the given expression could be typed in as (16*x^6*y^7)^(1/4), for instance.

I'm guessing you have to simplify the given expression. You could end up with

∜(16x ⁶y ⁷) = ∜(2⁴ x ⁴ x ² y ⁴ y ³)

… = 2xy ∜(x ² y ³)

(assuming x and y are positive)