Question

Ashley thinks of a number She squares it, takes away the square root of 64, divides it all by the cube root of 512, and then finally she adds 8 quarters. Her answer is 4. What number did she start with?

Answer 1

If a number is squared then sq. root of 64 is taken out, divided by cube root of 512 and added by 8/4 and gets an answer as 4 then the number is √24.

Step-by-step explanation:

Let’s assume that the number Ashley’s thinks of is “x”.

According to the data in the question, let's solve for x step by step:

1. Ashley squares the number she thought i.e., “x²”.
2. She takes away the square root of 64 from the number so: [x² - √64] = [x² – 8]
3. She divides the whole term in step 2 by the cube root of 512: [(x² - 4)/∛512] = [(x² - 8)/8]
4. Then she finally adds 8 quarters i.e., [(x² - 8)/8] + 8(1/4) = [(x² - 8)/8] + 2

It is also given that the final answer Ashley gets is 4.

∴ [(x² - 8) / 8] + 2  = 4

⇒  (x² - 8) / 8  = 2

⇒ x² - 8 = 16

⇒ x² = 24

⇒ x = √24

Thus, Ashley started with √24.

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