Question

find the positive square root of root 50 + root 48

Answer 1

Answer:

Step-by-step explanation:

Concept:

A positive number has two square roots, one positive and the other negative, that are diametrically opposed. When we talk about the square root of a positive integer, we usually mean the positive square root. An integer's square roots are algebraic integers, more specifically quadratic integers.

Given:

The square root is $\sqrt{50} +\sqrt{48}$

Find :

Lets find the positive square root of $\sqrt{50} +\sqrt{48}$.

Solution:

Consider,

$\sqrt{50} +\sqrt{48}$

Now ,

$\begin{aligned}&\sqrt{50}+\sqrt{48}=5 \sqrt{2}+4 \sqrt{3} \\&=\sqrt{2}[5+2 \cdot \sqrt{2} \cdot \sqrt{3}] \\&=\sqrt{2}(\sqrt{3}+\sqrt{2})^{2} \\&\therefore \sqrt{\sqrt{50}+\sqrt{48}} \\&=2^{1 / 4}(\sqrt{3}+\sqrt{2})\end{aligned}$

The positive square root of $\sqrt{50} +\sqrt{48}$ is $2^{1 / 4}(\sqrt{3}+\sqrt{2})$.

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Answer 2

Answer:

Answer is :-   $(2)^(1/4) (\sqrt{2} + \sqrt{3)}$

Step-by-step explanation:

Given :- $\sqrt{50} +\sqrt{48 }$

To find :- $\sqrt{\sqrt{50} +\sqrt{48} }$

Solution :-

Step 1) $\sqrt{50} = \sqrt{25*2}=5\sqrt{2}$

Step 2) $\sqrt{48} = \sqrt{16*3} = 4\sqrt{3}$

Step 3) $\sqrt{50} +\sqrt{48} = 5\sqrt{2} + 4\sqrt{3\\} = \sqrt{2} ( 5 + 2*\sqrt{2}*\sqrt{3} ) \\ = \sqrt{2} ( \sqrt{2} + \sqrt{3} )^2$

Step 4) $\sqrt{\sqrt{50} +\sqrt{48} } = ( \sqrt{\sqrt{2}*(\sqrt{2}+\sqrt{3})^2 }$

by rule of indices .

$(a^n)^m = a^(nm)$

therefore , equation becomes  $(2)^(1/4) (\sqrt{2} + \sqrt{3)}$

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