Radicals and exponents practice according to the exponent rules what is a rational exponent of an expression of three square root 5 enter your response in fraction form

Answer 1

To express the square root of 5 with a rational exponent, we first recognize that the square root can be rewritten in terms of exponents.

The square root of a number can be expressed as that number raised to the power of \( \frac{1}{2} \). Therefore:

\[ \sqrt{5} = 5^{\frac{1}{2}} \]

Now, if we want the expression "three times the square root of 5," we can write it as:

\[ 3 \sqrt{5} = 3 \cdot 5^{\frac{1}{2}} \]

This gives us the final expression in terms of a rational exponent:

\[ 3 \cdot 5^{\frac{1}{2}} \]

So, the rational exponent of "three square root 5" in different contexts may also be left as is or explicitly noted, but it fundamentally involves the expression \(3 \cdot 5^{\frac{1}{2}}\). If you're seeking just the exponent of the square root, it is \( \frac{1}{2} \).