6^((1)/(2))+6^((3)/(2)) Which of the following values is equal to the given value? Choose 1 answer: (A) sqrt222 (B) 7sqrt6 (c) 6^((3)/(4)) (D) 36

Understanding the given expressions: Understand the given expressions. 6^((1)/(2)) is the square root of 6, which can be written as √6. 6^((3)/(2)) is the same as (6^(1/2))^3, which means the square root of 6 cubed, or (√6)^3.Simplifying the expressions: Simplify the expressions. √6 is already in its simplest form. (√6)^3 means √6 * √6 * √6, which is 6 * √6 because √6 * √6 = 6.Adding the simplified expressions: Add the simplified expressions. 6^((1)/(2)) + 6^((3)/(2)) = √6 + 6 * √6. This can be written as 1√6 + 6√6, which is 7√6.Matching the result with the choices: Match the result with the given choices. The result from Step 3 is 7√6, which corresponds to choice (B) 7√6.

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6^((1)/(2))+6^((3)/(2))
Which of the following values is equal to the given value?
Choose 1 answer:
(A)
sqrt222
(B)
7sqrt6
(c)
6^((3)/(4))
(D) 36

$6^{\frac{1}{2}}+6^{\frac{3}{2}}$ $\newline$ Which of the following values is equal to the given value? $\newline$ Choose $1$ answer: $\newline$ (A) $\sqrt{222}$ $\newline$ (B) $7 \sqrt{6}$ $\newline$ (C) $6^{\frac{3}{4}}$ $\newline$ (D) $36$

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Math Problems

Algebra 1

Compare linear and exponential growth

Full solution

6^{\frac{1}{2}}+6^{\frac{3}{2}}

\newline

Which of the following values is equal to the given value?

\newline

Choose

1

answer:

\newline

(A)

\sqrt{222}

\newline

(B)

7 \sqrt{6}

\newline

(C)

6^{\frac{3}{4}}

\newline

(D)

36

Understanding the given expressions: Understand the given expressions. $\newline$ $6^{\left(\frac{1}{2}\right)}$ is the square root of $6$ , which can be written as $\sqrt{6}$ . $\newline$ $6^{\left(\frac{3}{2}\right)}$ is the same as $\left(6^{\frac{1}{2}}\right)^3$ , which means the square root of $6$ cubed, or $\left(\sqrt{6}\right)^3$ .
Simplifying the expressions: Simplify the expressions. $\newline$ $\sqrt{6}$ is already in its simplest form. $\newline$ $(\sqrt{6})^3$ means $\sqrt{6} \times \sqrt{6} \times \sqrt{6}$ , which is $6 \times \sqrt{6}$ because $\sqrt{6} \times \sqrt{6} = 6$ .
Adding the simplified expressions: Add the simplified expressions. $\newline$ $6^{\left(\frac{1}{2}\right)} + 6^{\left(\frac{3}{2}\right)} = \sqrt{6} + 6 \cdot \sqrt{6}$ . $\newline$ This can be written as $1\sqrt{6} + 6\sqrt{6}$ , which is $7\sqrt{6}$ .
Matching the result with the choices: Match the result with the given choices. $\newline$ The result from Step $3$ is $7\sqrt{6}$ , which corresponds to choice (B) $7\sqrt{6}$ .