Question

prove that 5+ root5 is an irrational number. ​

Answer 1

Step-by-step explanation:

Let length of rectangle=lcm

breadth of rectangle= bcm

Given length is 3 times its breadth

i.e. l= 3×b

Perimeter of the rectangle= 120 cm

i.e.2×( l+ b)=120

2×(3×b+ b)=120

2×(4×b)=120

8×b=120

b= 15 cm

SO SORRY DEAR FOR MY WRONG ANSWER BUT YE ZARURI THA plz understand ......

Answer 2

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To Prove :-

$\large\bold\red{5 + \sqrt{5} \: is \: irrational. }$

$\large\bold\green{Solution}$

Let us suppose that 5 + √5 is not irrational

=> 5 + √5 is rational.

Let we suppose that 5 + √5 = x/y, where x and y are positive integers such that HCF of a and b is 1.

$\sqrt{5} = \frac{x}{y} - 5 \\ \sqrt{5} = \frac{x - 5y}{y}$

Now, as x and y are intergers, so x - 5y is also an integer.

$= > \frac{x - 5y}{5} \: is \: a \: rational \: number \\ = > \: \sqrt{5} \: is \: rational.$

which is contradiction to the fact that √5 is irrational.

Hence, our assumption is wrong.

$\small\bold\red{ = > \: 5 + \sqrt{5} \: is \: irrational. }$

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