1)prove that √ 3+√ 5 is an irrational number 2)how to mark√ 7 and √ 3.5 on different number lines? THANK YOU
Answers
Hi friend!!
Let √3+√5 be a rational number.
A rational number can be written in the form of p/q where p,q are integers.
√3+√5 = p/q
√3 = p/q-√5
Squaring on both sides,
(√3)² = (p/q-√5)²
3 = p²/q²+√5²-2(p/q)(√5)
√5×2p/q = p²/q²+5-3
√5 = (p²+2q²)/q² × q/2p
√5 = (p²+2q²)/2pq
p,q are integers then (p²+2q²)/2pq is a rational number.
Then √5 is also a rational number.
But this contradicts the fact that √5 is an irrational number.
So,our supposition is false.
Therefore, √3+√5 is an irrational number
ii) Following steps:
Draw a number line as shown in figure.
From point , take point on left name as and take point on right name as.
Bisect the line to get mid point of the line name as.
Take as a center and as radius draw an semi circle.
Using set-square draw perpendicular line through point which touch the circle line at
Answer:
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