Find the square root of: frac{7}{4} + sqrt{3} | vedclass

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Question

(A) To find the square root of $\frac{7}{4} + \sqrt{3}$,we express it in the form $(a + b)^2 = a^2 + b^2 + 2ab$.We can rewrite the expression as $\fra

Vedclass · Accepted Answer

$\frac{\sqrt{3}}{2} + 1$

Vedclass · Answer

(A) To find the square root of $\frac{7}{4} + \sqrt{3}$,we express it in the form $(a + b)^2 = a^2 + b^2 + 2ab$.We can rewrite the expression as $\frac{7}{4} + 2 \cdot \frac{\sqrt{3}}{2}$.Let the square root be $(a + b)$. Then $(a + b)^2 = a^2 + b^2 + 2ab = \frac{7}{4} + 2 \cdot \frac{\sqrt{3}}{2}$.Comparing the terms,we have $2ab = 2 \cdot \frac{\sqrt{3}}{2}$,so $ab = \frac{\sqrt{3}}{2}$.Also,$a^2 + b^2 = \frac{7}{4}$.Let $a = \frac{\sqrt{3}}{2}$ and $b = 1$. Then $a^2 + b^2 = \frac{3}{4} + 1 = \frac{7}{4}$.Thus,$\frac{7}{4} + \sqrt{3} = (\frac{\sqrt{3}}{2} + 1)^2$.Therefore,the square root is $\frac{\sqrt{3}}{2} + 1$.

Find the square root of: $\frac{7}{4} + \sqrt{3}$

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