Question

What is the radical form of each of the given expressions?

Drag the answer into the box to match each expression.

4 1/7------------_____
4 7/2-----------_____
7 1/4------------_____
7 1/2------------_____

please fill in the _ here are the options

sqrt (7^2) , sqrt (4^7) , ^7 sqrt (4) , ^4 sqrt (7) , sqrt (7)

Answer 1

When you have fractions in the exponent, the denominator is the root and the numerator is the power on the number inside the root.

4^(1/7) = ⁷√(4)
4^(7/2) = √(4)^7
7^(1/4) = ⁴√(7)
7^(1/2) = √(7)

Answer 2

Radical form refers to a form of an algebraic expression in which we have a number or an expression underneath a radical.

Any algebraic expression involving exponents then, we can write it in radical form based on the fact that
`x^{(a)/(n)}` is equivalent to the nth root of
`x^a` i.e,

`x^{(a)/(n)}` =
`\sqrt[n]{x^a}`

Now, Consider the expression:

`4^{(1)/(7)} = \sqrt[7]{4}`

`4^{(7)/(2)} = \sqrt[2]{4^7}`

`7^{(1)/(4)} = \sqrt[4]{7}`

`7^{(1)/(2)} = \sqrt[2]{7}`