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if $7a = 8\sqrt{7}$ , what is the value of $a$ ?

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Find limits using power and root laws

Full solution

Q. if

7a = 8\sqrt{7}

, what is the value of

a

?

Write Equation: Write down the given equation. $\newline$ We are given that $7a = 8\sqrt{7}.$
Isolate Variable: Isolate the variable $a$ . To find the value of $a$ , we need to isolate it on one side of the equation. We can do this by dividing both sides of the equation by $7$ . $a = \frac{8\sqrt{7}}{7}$
Simplify Expression: Simplify the expression. $\newline$ The $7$ in the denominator cancels out with the $7$ inside the square root in the numerator, since $\sqrt{7}$ is the same as $7^{1/2}$ and $7^{1/2} / 7 = 7^{-1/2}$ . $\newline$ $a = 8 / 7^{1/2}$ $\newline$ $a = 8 / \sqrt{7}$
Rationalize Denominator: Rationalize the denominator (optional). $\newline$ To express the answer in a more standard form, we can multiply the numerator and denominator by $\sqrt{7}$ to get rid of the square root in the denominator. $\newline$ $a = \frac{8\sqrt{7}}{7}$
Check for Errors: Check for any mathematical errors. $\newline$ Re-evaluate the steps to ensure there are no errors in the calculations. $\newline$ No errors found.

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