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# Find the positive square root of $\sqrt{48}-\sqrt{45}$?

Last updated date: 19th Sep 2024
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Hint: First find the square root of the numbers and then find the common term in the square-root after finding the square root frame the square root in such a way that one get a root of power four fraction in the answer to find the positive root.

Complete step by step solution:
To find the value of the square root of the numbers given in the equation we get the value of the square root as common numbers while searching for numbers we see that the square root of the number is given as:
$\sqrt{48}-\sqrt{45}=4\sqrt{3}-3\sqrt[{}]{5}$
Now to convert the value in simpler form we change the square root of the number from the term given above as:
$\Rightarrow 4\sqrt{3}-3\sqrt[{}]{5}$
Taking a common fraction $\dfrac{\sqrt{3}}{2}$ from the two values in the above equation, we get the square root value as:
$\Rightarrow \dfrac{\sqrt{3}}{2}\left( 8-2\sqrt{15} \right)$
Now we separate the power given in the question to find the value of the square root in fraction as:
$\Rightarrow 4\sqrt{3}-3\sqrt[{}]{5}$
A common fraction $\dfrac{\sqrt{3}}{2}$ from the two values in the above equation, we get the square root value as:
$\Rightarrow \dfrac{\sqrt{3}}{2}\left( 8-2\sqrt{15} \right)$
Now we separate the power given in the question to find the value of the square root in fraction as:
$\Rightarrow 4\sqrt{3}-3\sqrt[{}]{5}$

Note: To simplify a square root : make the number inside a square root as small as possible.The positive number, when multiplied by itself, represents the square of the number. The square root of the square of a positive number gives the original number