Question

answer this fast pls. ... maths
best answer = brainliest and 5 thanks...​

Answer 1

Answer:

1 = 4√2 is an irrational number because if we find out the value of √2 we will get it in decimal so when we will get it in decimal it is considered as an irrational number

2 = let us suppose 3 + root 5 is rational as p,q and 3 are integers p -3q/3 is a rational number hence 3 + root 5 is an irrational number

3 = we know that √4 = 2 and , √5 = (2)^2+(1)^2 mark point ''A' representing 2 on number line , now construct 'AB' of unit length perpendicular to 'OA' then, taking 0 as a centre and 'OB' as radius, draw an Arc intersecting number line at C so, C is representing √5 here we have represented root 5 on number line

now we have to represent root 10 on number line take a line segment 'OA' = 3 unit on the x-axis ( consider one unit = 2 cm ) draw a perpendicular on 0 And draw a line OC = 1 unit now join AC with root 10 take A as centre and AC as radius , draw an Arc which cuts the x-axis at point E the line segment AC represents √10 units

here is your answer I hope it may help you mark me as brainliest and give thanks as you had said if you think my answer is best ....

Answer 2

Explanation:

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a] part...

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〰Given that :- 4√2

〰To prove :- 4√2 is an irrational number .

⚫We shall prove this by the method of Contraction . so let us assume that 4√2 is a Rational Number .

4√2 = r

√2 = r/4

Now, we know √2 is an irrational number.

So RHS { r/4 } cannot be rational . As then the equation will be false .

So our Assumption is Wrong .

Hence , 4√2 is an irrational number .

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b] part.....

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Let us assume that 3 + √5 is a rational number.

Now,

3 + √5 = (a ÷ b)

[Here a and b are co-prime numbers]

√5 = [(a ÷ b) - 3]

√5 = [(a - 3b) ÷ b]

Here, {(a - 3b) ÷ b} is a rational number.

But we know that √5 is a irrational number.

So, {(a - 3b) ÷ b} is also a irrational number.

So, our assumption is wrong.

3 + √5 is a irrational number.

Hence, proved.

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hope it helps you sindhu;!plz Mark as brainliest answer!;)

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