Determine the exact value of (Square Root of Square Root)

In summary, the exact value of a number in math refers to the precise numerical value, not an approximation. The square root of a number is a value that, when multiplied by itself, gives the original number. The square root of a square root is the number that, when multiplied by itself and then multiplied by itself again, gives the original number. To determine the exact value of the square root of a square root, you can use the property that states the square root of a product is equal to the product of the square roots. The exact value of the square root of a square root of a perfect square is the square root of the perfect square itself.
  • #1
n3w ton
19
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Determine the exact value of... (Square Root of Square Root)

I was looking through my textbook and saw a interesting question, I attempted but couldn't get it. (The Answer in Back of Text Book Was Different From Mine..)

Question
Determine the exact value of...

√10+√10+√10...


I tried typing it as well as I can , I uploaded image of question just in case :D

Determine the exact value of:
0sVBk.jpg
 
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  • #2


Let

[tex]x=\sqrt{10+\sqrt{10+\sqrt{10+...}}}[/tex]

What is

[tex]x^2-10[/tex]

Does this give you an equation that you can solve??
 

What is the definition of "exact value" in math?

The exact value of a number is the precise numerical value, as opposed to an approximation or estimation.

What is the square root of a number?

The square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 9 is 3, because 3 x 3 = 9.

What is the square root of a square root?

The square root of a square root is the number that, when multiplied by itself and then multiplied by itself again, gives the original number. For example, the square root of the square root of 16 is 2, because 2 x 2 x 2 x 2 = 16.

How do you determine the exact value of the square root of a square root?

To determine the exact value of the square root of a square root, you can use the property of square roots that states the square root of a product is equal to the product of the square roots. For example, the square root of the square root of 16 is equal to the square root of 4 times the square root of 4, which is 2 x 2 = 4.

What is the exact value of the square root of a square root of a perfect square?

The exact value of the square root of a square root of a perfect square is the square root of the perfect square itself. For example, the exact value of the square root of the square root of 100 is the square root of 100, which is 10.

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