Can the No $4\sqrt{4-2\sqrt {3}}+\sqrt{97-56\sqrt 3}$ be an Integer?

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In summary, the conversation discusses a mathematical expression that can be simplified to $4\sqrt{1-\sqrt{3}}+\sqrt{1+\sqrt{3}}$, and explains that an integer is a whole number without a fractional or decimal component. It is mentioned that the simplified expression can be an integer if the terms inside the square root are perfect squares. To determine if the expression is an integer, one can simplify the terms inside the square root and check if they are perfect squares.
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solakis1
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Can the No :$4\sqrt{4-2\sqrt {3}}+\sqrt{97-56\sqrt 3}$ be an iteger ,if yes prove it if no then prove it again
 
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integer ...

$4-2\sqrt{3} = 3 - 2\sqrt{3} +1 = (\sqrt{3} -1)^2$

$97-56\sqrt{3} = 49 - 2(28\sqrt{3}) + 48 = (7 - 4\sqrt{3})^2$

$4\sqrt{(\sqrt{3}-1)^2} + \sqrt{(7-4\sqrt{3})^2} = 4\sqrt{3}-4 + 7 -4\sqrt{3} = 3$
 
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very good ,excellent
 

FAQ: Can the No $4\sqrt{4-2\sqrt {3}}+\sqrt{97-56\sqrt 3}$ be an Integer?

What is the equation being asked about?

The equation in question is No $4\sqrt{4-2\sqrt {3}}+\sqrt{97-56\sqrt 3}$.

Is the equation solvable?

Yes, the equation is solvable since it is a mathematical expression that follows the rules of algebra.

What is the significance of the numbers and symbols in the equation?

The numbers and symbols in the equation represent mathematical operations and values. The square root symbol (√) indicates the square root of a number, and the caret symbol (^) is used to represent exponents. The numbers in the equation are constants, meaning they have a fixed value.

Can the result of the equation be an integer?

Yes, it is possible for the result of the equation to be an integer. However, it is not guaranteed since the equation contains square roots and exponents, which can result in irrational numbers.

How can the equation be solved to determine if the result is an integer?

The equation can be solved by simplifying the expression and then evaluating it. If the result is a whole number, then it is an integer. If the result is a decimal or fraction, then it is not an integer.

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