Questions: (a) Using exponential notation, we can write the cube root of 10 as . (b) Using radicals, we can write 10 to the power of 1/2 as . (c) Is there a difference between the square root of 10 squared and (the square root of 10) squared? Yes No

(a) Using exponential notation, we can write the cube root of 10 as .
(b) Using radicals, we can write 10 to the power of 1/2 as .
(c) Is there a difference between the square root of 10 squared and (the square root of 10) squared?
Yes
No

Transcript text: (a) Using exponential notation, we can write $\sqrt[3]{10}$ as $\square$ . (b) Using radicals, we can write $10^{1 / 2}$ as $\square$ . (c) Is there a difference between $\sqrt{10^{2}}$ and $(\sqrt{10})^{2}$ ? Yes No

Solution

Solution Steps

Solution Approach

(a) To express the cube root of 10 using exponential notation, we use the fact that the cube root of a number $x$ can be written as $x^{1/3}$ .

(b) To express $10^{1/2}$ using radicals, we use the fact that $x^{1/2}$ is the same as the square root of $x$ .

(c) To determine if there is a difference between $\sqrt{10^2}$ and $(\sqrt{10})^2$ , we need to simplify both expressions and compare the results.

Step 1: Expressing

\sqrt[3]{10}

in Exponential Notation

Using exponential notation, we can write the cube root of 10 as: $\sqrt[3]{10} = 10^{1/3} \approx 2.1544$

Step 2: Expressing

10^{1/2}

Using Radicals

Using radicals, we can express $10^{1/2}$ as: $10^{1/2} = \sqrt{10} \approx 3.1623$

Step 3: Comparing

\sqrt{10^2}

and

(\sqrt{10})^2

We simplify both expressions: $\sqrt{10^2} = 10$ $(\sqrt{10})^2 = 10$ However, due to floating-point precision, we find: $\sqrt{10^2} = 10.0 \quad \text{and} \quad (\sqrt{10})^2 \approx 10.0000$ Thus, while they are mathematically equal, the comparison shows a slight difference in their computed values.