Question

Prove that
√+√+=

CAN SOMEONE PLEASE ANSWER QUICK
WOULD BE BETTER IF DONE IN AN ATTACHMENT

Answer 1

√+√=?

so,

we know that ,

if two same number are in under root = in root is removed.

let's consider √+√ =x

hence.,

there is no number in root .

so there is 1.

➡️√1+√1 =x

➡️√2 =x

• to remove root squaring on both sides

$=>\sqrt2^{2}=x^{2} \\ => 2 =x^{2} \\ =>x^{2}=2 \\ x = \sqrt2 \\ =>x \sqrt1×1 \\ => x=1 \: <strong>prov</strong><strong>£</strong><strong>d</strong>.$

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Answer 2

Step-by-step explanation:

I have proved in earlier exercises of this book that 2–√ and 3–√ are irrational. Then, the sum of two irrational numbers is an irrational number. Thus, 2–√+3–√ is irrational. My first question is, is this reasoning correct?

Secondly, the book wants me to use the fact that if n is an integer that is not a perfect square, then n−−√ is irrational. This means that 6–√ is irrational. How are we to use this fact? Can we reason as follows:

6–√ is irrational

⇒2⋅3−−−√ is irrational.

⇒2–√⋅3–√ is irrational

⇒2–√ or 3–√ or both are irrational.

⇒2–√+3–√ is irrational.

Is this way of reasoning correct?