Chapter 12, Problem 1RE

To determine

To write: The square root of 49 in radical notation and exponential notation.

Answer to Problem 1RE

The raidcal notation for square root of 49 is $\underset{\_}{\sqrt{49}}$ and the exponential notation for square root of 49 is $\underset{\_}{{49}^{\frac{1}{2}}\text{ or }{49}^{0.5}}$.

Explanation of Solution

Procedure used:

To write roots using radical and exponential notation:

“1. Identify the index of the root.

2. For radical notation, place the index of the root in the portion of the radical sign with the radicand under the bar portion of the sign. The index 2 for square roots does not have to be written.

3. For exponential notation, write the radicand as the base and index of the roots as the denominator of a fraction exponent that thas a numerator of 1. The decimal equivalent of the fractional exponent can also be used”.

Calculation:

In square root of 49, it is observed that the radicand is 49 and index of the root is 2.

Thus, the radical notation for square root of 49 represented as $\sqrt{49}$.

Write the exponential notation for square root of 49 as follows.

The base of the exponent is 49 and the denominator of the fractional exponent is 2.

That is, $\text{Square root of 49}={49}^{\frac{1}{2}}\text{ or }{49}^{0.5}$.

Therefore, the radical notation for square root of 49 is $\underset{\_}{\sqrt{49}}$ and the exponential notation for square root of 49 is $\underset{\_}{{49}^{\frac{1}{2}}\text{ or }{49}^{0.5}}$.