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# Solving for A

+2
213
3

If $$(4-a)^3 = 32$$, then what is $$a$$?

Answer is $$a = 4-2\sqrt{4}$$.

I just need work finding the solution.

Jul 24, 2019

#1
+5

$$(4-a)^3\ =\ 32$$

Take the cube root of both sides of the equation.

$$\sqrt{(4-a)^3}\ =\ \sqrt{32}$$

Simplify the left side with the rule  $$\sqrt{n^3}\ =\ n$$

$$4-a\ =\ \sqrt{32}$$

We can rewrite  32  like this because  32 = 2 * 2 * 2 * 2 * 2

$$4-a\ =\ \sqrt{2\cdot2\cdot2\cdot2\cdot2}$$

We can rewrite the right side again like this...

$$4-a\ =\ \sqrt{2\cdot2\cdot2}\cdot\sqrt{2\cdot2}$$

And   2 * 2 * 2  =  23   and   2 * 2  =  4

$$4-a\ =\ \sqrt{2^3}\,\cdot\,\sqrt{4}$$

Simplify  $$\sqrt{2^3}$$  again with the rule  $$\sqrt{n^3}\ =\ n$$

$$4-a\ =\ 2\,\cdot\,\sqrt{4}$$

$$4-a\ =\ 2\sqrt{4}$$

Add  a  to both sides of the equation.

$$4\ =\ 2\sqrt{4}+a$$

Subtract  $$2\sqrt{4}$$  from both sides of the equation.

$$4-2\sqrt{4}\ =\ a$$

$$a\ =\ 4-2\sqrt{4}$$-

Jul 24, 2019
#2
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Nice!

Nickolas  Jul 24, 2019
#3
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(4-a)^3 = 32      cube root both sides   (note that 32 = 2^5 )

(4-a) = cubrt(2^5)      Simplify the right side

(4-a) = 2 cubrt(4)      Add 'a' to both sides and subtract 2 cubrt(4) from both sides

4- 2 cubrt(4) = a

Jul 24, 2019