What is the geometric mean of 7 and 12 ? (F) 1(5)/(7) G 9.5 (H) 2sqrt21 (1) 4sqrt21

Understand Geometric Mean: Understand the concept of geometric mean. The geometric mean of two numbers is the square root of their product.Calculate Product: Calculate the product of the two numbers. Product of 7 and 12 = 7 * 12 = 84Find Square Root: Find the square root of the product to get the geometric mean. Geometric mean = √84Simplify Square Root: Simplify the square root. √84 can be simplified by factoring out perfect squares. 84 = 4 * 21, and 4 is a perfect square. So, √84 = √(4 * 21) = √4 * √21 = 2√21

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What is the geometric mean of 7 and 12 ?
(F)
1(5)/(7)
G 9.5
(H)
2sqrt21
(1)
4sqrt21

What is the geometric mean of $7$ and $12$ ? $\newline$ (F) $1\frac{5}{7}$ $\newline$ (G) $9.5$ $\newline$ (H) $2\sqrt{21}$ $\newline$ (I) $4\sqrt{21}$

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Q. What is the geometric mean of

7

and

12

\newline

(F)

1\frac{5}{7}

\newline

(G)

9.5

\newline

(H)

2\sqrt{21}

\newline

(I)

4\sqrt{21}

Understand Geometric Mean: Understand the concept of geometric mean. The geometric mean of two numbers is the square root of their product. That is, if the numbers are $a$ and $b$ , their geometric mean is $\sqrt{a \times b}$ .
Calculate Product: Calculate the product of the two numbers. $\newline$ Product of $7$ and $12$ = $7 \times 12 = 84$
Find Square Root: Find the square root of the product to get the geometric mean. $\newline$ Geometric mean = $\sqrt{84}$
Simplify Square Root: Simplify the square root. $\newline$ $\sqrt{84}$ can be simplified by factoring out perfect squares. $\newline$ $84 = 4 \times 21$ , and $4$ is a perfect square. $\newline$ So, $\sqrt{84} = \sqrt{4 \times 21} = \sqrt{4} \times \sqrt{21} = 2\sqrt{21}$