Question

1. If 7x5x3x2 + 3 is composite number? Justify your answer
2. Show that any positive odd integer is of the form 4+1 or 4q+3 where q is a positive integer
3. Prove that V2 + v5 is irrational
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Answer 1

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Answer 2

1. 7×5×3×2+3

3(7×5+1)

as the numbers are prime number and multiple of two number therefore they are composite number

2. prove: 4q+1 and 4q+3 is odd positive

a=bq+r. 0 <r <4

put value of r as 1

a=4q +1

again put value of r as 3

a=4q+3

for values of q , 4q+1 and 4q+3 is always odd.

3.prove: V2+V5

let V2+V5 BE A rational no

V2+V5=a

squaring both sides

(V2+V5)^2=a2

2+5+2V10=a2

7+2V10=a2

V10=a2-7/2

a2-7/2 is a rational no

therefore V10 will be rational

but we know V10 is irrational

therefore our assumption is wrong and V2+V5 is irrational