Q4 of 40 Page 34

Show that 5 + √7 is an irrational number.

Let us assume that 5 + √7 is a rational number



where, b≠0 and a, b are integers




∵ a, b are integers ∴ a – 5b and b are also integers


is rational which cannot be possible ∵ which is an irrational number


∵ it is contradicting our assumption ∴ the assumption was wrong


Hence, 5 + √7 is an irrational number


More from this chapter

All 40 →
2

Write the following numbers in p/q form.

i. 0.555 ii.


iii. 9.315 315 ... iv. 357.417417...


v.

3

Write the following numbers in its decimal form.

i. -5/7 ii. 9/11


iii. √5 iv. 121/13


v. 29/8

 5

Write the following surds in simplest form.

i. ii.

6

Write the simplest form of rationalizing factor for the given surds.

i. √32 ii. √50


iii. √27 iv. 3/5√10


v. 3√72 vi. 4√11