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sqrt(25h^(2)+144h^(2))+root(3)(h^(2))
Which of the following expressions is equivalent to the given expression?
Choose 1 answer:
(A)
13 h+h^((2)/(3))
(B)
14 h
(C)
17 h+h^((2)/(3))
(D)
18 h

$\sqrt{25 h^{2}+144 h^{2}}+\sqrt[3]{h^{2}}$ $\newline$ Which of the following expressions is equivalent to the given expression? $\newline$ Choose $1$ answer: $\newline$ (A) $13 h+h^{\frac{2}{3}}$ $\newline$ (B) $14 h$ $\newline$ (C) $17 h+h^{\frac{2}{3}}$ $\newline$ (D) $18 h$

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Compare linear, exponential, and quadratic growth

Full solution

Q.

\sqrt{25 h^{2}+144 h^{2}}+\sqrt[3]{h^{2}}

\newline

Which of the following expressions is equivalent to the given expression?

\newline

Choose

1

answer:

\newline

(A)

13 h+h^{\frac{2}{3}}

\newline

(B)

14 h

\newline

(C)

17 h+h^{\frac{2}{3}}

\newline

(D)

18 h

Simplify expression inside square root: Simplify the expression inside the square root. $\newline$ We have $\sqrt{25h^2 + 144h^2}$ . Combine like terms by adding the coefficients of $h^2$ . $\newline$ $25h^2 + 144h^2 = (25 + 144)h^2 = 169h^2$
Take square root of simplified expression: Take the square root of the simplified expression. $\newline$ Now we have $\sqrt{169h^2}$ . Since $169$ is a perfect square and $h^2$ is also a perfect square, we can take the square root of both. $\newline$ $\sqrt{169h^2} = \sqrt{169} \times \sqrt{h^2} = 13h$
Simplify cube root of $h^2$ : Simplify the cube root of $h^2$ . $\newline$ The cube root of $h^2$ is $\sqrt[3]{h^2}$ . This expression cannot be simplified further and remains as is.
Combine results from Step $2$ and Step $3$ : Combine the results from Step $2$ and Step $3$ . $\newline$ We have $13h$ from the square root and $\sqrt[3]{h^2}$ from the cube root. Combine these to get the final expression. $\newline$ $13h + \sqrt[3]{h^2} = 13h + h^{\frac{2}{3}}$

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