Question

Prove that √3 + √5 is an irrational number.​

Answer 1

Answer:

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Step-by-step explanation:

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1

Secondary School Math 5 points

Prove that root 3 plus root 5 is irrational

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Answers

Let √3+√5 be any rational number x

x=√3+√5

squaring both sides

x²=(√3+√5)²

x²=3+5+2√15

x²=8+2√15

x²-8=2√15

(x²-8)/2=√15

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Answer 2

Step-by-step explanation:

TO PROVE THAT ROOT 3+ ROOT 5 IS A IRRATIONAL NUMBER.

LET ROOT 3 + ROOT 5 ARE RATIONAL NUMBER IN THE FORM OF a by b.

$\sqrt{3} + \sqrt{5} = \frac{a}{b} \\ \\ squaring \: both \: sides \\ \\ { (\sqrt{3} + \sqrt{5} ) }^{2} = { \frac{a}{b} }^{2} \\ \\ 3 + 5 + 2 \times \sqrt{3} \times \sqrt{5} = { \frac{a}{b} }^{2} \\ \\ 8 + 2 \sqrt{15} = \frac{ {a}^{2} }{ {b}^{2} } \\ \\ 2 \sqrt{15} = \frac{ {a}^{2} }{ {b}^{2} } - 8 \\ \\ 2 \sqrt{15} = \frac{ {a}^{2} - 8 {b}^{2} }{ {b}^{2} } \\ \\ \sqrt{15} = \frac{ {a}^{2} - 8 {b}^{2} }{ {b}^{2} } \times 2$

HENCE HERE CONTRADICTION ARISES AS WE KNOW THAT ROOT 15 IS IRRATIONAL NUMBER

HENCE PROVED

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