Question

please answer this question​

Answer 1

Answer

Let's simplify it step by step.

$(\dfrac{2}{3} \sqrt{5} - \dfrac{1}{2} \sqrt{2} + 6\sqrt{11}) + \dfrac{1}{3}\sqrt{5} + \dfrac{3}{2}\sqrt{2} - \sqrt{11})$

Step 1: Open brackets.

⇒ $(\dfrac{2}{3} \sqrt{5} - \dfrac{1}{2} \sqrt{2} + 6\sqrt{11}) + \dfrac{1}{3}\sqrt{5} + \dfrac{3}{2}\sqrt{2} - \sqrt{11})$

⇒ $\dfrac{2}{3} \sqrt{5} - \dfrac{1}{2} \sqrt{2} + 6\sqrt{11}+ \dfrac{1}{3}\sqrt{5} + \dfrac{3}{2}\sqrt{2} - \sqrt{11}$

Step 2: Combine Like Terms.

⇒ $\dfrac{2}{3} \sqrt{5} - \dfrac{1}{2} \sqrt{2} + 6\sqrt{11}+ \dfrac{1}{3}\sqrt{5} + \dfrac{3}{2}\sqrt{2} - \sqrt{11}$

⇒ $\dfrac{2}{3} \sqrt{5}+ \dfrac{1}{3}\sqrt{5} - \dfrac{1}{2} \sqrt{2} + \dfrac{3}{2}\sqrt{2} + 6\sqrt{11}- \sqrt{11}$

Step 3: Simplify the equation.

⇒ $\dfrac{2}{3} \sqrt{5}+ \dfrac{1}{3}\sqrt{5} - \dfrac{1}{2} \sqrt{2} + \dfrac{3}{2}\sqrt{2} + 6\sqrt{11} - \sqrt{11}$

⇒ $\dfrac{3}{3} \sqrt{5} + \dfrac{2}{2} \sqrt{2}+ 6\sqrt{11} - \sqrt{11}$

⇒ $1 \sqrt{5} + 1 \sqrt{2}+ 6\sqrt{11} - 1\sqrt{11}$

⇒ $\sqrt{5} + \sqrt{2}+ 5\sqrt{11}$

∴ $\bf (\dfrac{2}{3} \sqrt{5} - \dfrac{1}{2} \sqrt{2} + 6\sqrt{11}) + \dfrac{1}{3}\sqrt{5} + \dfrac{3}{2}\sqrt{2} - \sqrt{11}) = \sqrt{5} + \sqrt{2}+ 5\sqrt{11}$

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Additional Information

Rational Numbers ⇒ Numbers that can be represented in p/q form where p and q are integers and q ≠ 0 are known as rational numbers.

They can be terminating, and non-terminating and recurring (repeating).

Example → 1/2, 1/5, 9/8

Irrational Numbers ⇒ Numbers which we can't simplify and represent in p/q form where p and q are integers and q ≠ 0 are known as irrational numbers.

They are non-terminating and non-recurring (not repeating).

Example → π, 1.01001000100001...

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Answer 2

Question:-

• Simplify $\sf \: \bigg( \dfrac{2}{3} \sqrt{5} - \dfrac{1}{2} \sqrt{2} + 6 \sqrt{11} \bigg) \bigg( \dfrac{1}{3} \sqrt{5} + \dfrac{3}{2} \sqrt{2} - \sqrt{11} \bigg)$

Solution:-

Wait I will edit