HelpContactFor teachers and institutes
>_StemPy Lab
Mock TestsClassesGroups

>_StemPy Lab

Learn. Solve. Code the solutions. Test yourself.

Live examsFree mock exams, timed and rankedEveryone starts together, and your score and rank come the moment it ends.See the exams →

Learn

  • Physics
  • Chemistry
  • Mathematics
  • Biology
  • Python Programming
  • Statistics & Data Science
  • Classes
  • Groups

Practice

  • Problems
  • Quizzes
  • Mock Tests
  • Question Sets
  • Exams
  • Certificates
  • Python Labs
  • AI Practice Generator
  • Student-Created Tests

Community

  • Discussions
  • Resources
  • Notes
  • Blog

Account

  • Dashboard
  • My Content
  • Profile
  • Log in
© 2026 senLearn. All rights reserved.HelpAboutContactPrivacy PolicyTerms of UseRefund Policy
  1. Problems
  2. /Number Systems
  3. /Rational and Irrational Numbers

Rational and Irrational Numbers

Mathematics
+ Upload a Problem
More in Number SystemsRational and Irrational NumbersExponents and RadicalsDivisibility, HCF and LCM
25 problems
Type:
1.
A square garden has an area of 18 m². Find its side, its perimeter and its diagonal. New
High School (9–10), General · Rational and Irrational NumbersStemPy LabStemPy Lab
Medium
2.
Find √3 + √5 to three decimal places. Prove that √3 + √5 is irrational. New
High School (9–10), General · Rational and Irrational NumbersStemPy LabStemPy Lab
Hard
3.
Find the whole number m for which (3 + √m)(3 - √m) = 4. New
High School (9–10), General · Rational and Irrational NumbersStemPy LabStemPy Lab
Medium
4.
Prove that 5 - 3√2 is irrational. You may use the fact that √2 is irrational. New
High School (9–10), General · Rational and Irrational NumbersStemPy LabStemPy Lab
Easy
5.
Prove that the cube root of 2, the number whose cube is 2, is irrational. New
High School (9–10), General · Rational and Irrational NumbersStemPy LabStemPy Lab
Hard
6.
Among all fractions p/q with a bottom q from 1 to 10, which one is closest to √3 = 1.7320508…? New
High School (9–10), General · Rational and Irrational NumbersStemPy LabStemPy Lab
Medium
7.
6 is not a prime, but √6 is still irrational. Prove it by contradiction, using only the prime 2. New
High School (9–10), General · Rational and Irrational NumbersStemPy LabStemPy Lab
Hard
8.
Prove that √7 is irrational. Give a reason for every step. New
High School (9–10), General · Rational and Irrational NumbersStemPy LabStemPy Lab
Easy
9.
Prove that if 6 divides a², then 6 divides a. New
High School (9–10), General · Rational and Irrational NumbersStemPy LabStemPy Lab
Medium
10.
Prove that if n² is a multiple of 3, then n is a multiple of 3. New
High School (9–10), General · Rational and Irrational NumbersStemPy LabStemPy Lab
Medium
11.
Kabir works out n² - n + 11 for n = 1, 2, 3, … and finds 11, 13, 17, 23, 31 and so on, all primes. New
High School (9–10), General · Rational and Irrational NumbersStemPy LabStemPy Lab
Easy
12.
Give two irrational numbers whose sum is rational.
High School (9–10), General · Rational and Irrational Numbers, Exponents and RadicalsStemPy LabStemPy Lab
Medium
13.
Expand and simplify (√7 + √3)² and (2√2 - 1)².
High School (9–10), General · Rational and Irrational Numbers, Exponents and RadicalsStemPy LabStemPy Lab
Medium
14.
Multiply (2 + √5)(3 + √5) and write the answer in the form a + b√5.
High School (9–10), General · Rational and Irrational Numbers, Exponents and RadicalsStemPy LabStemPy Lab
Medium
15.
Say whether each number is rational or irrational.
High School (9–10), General · Rational and Irrational Numbers, Exponents and RadicalsStemPy LabStemPy Lab
Easy
16.
Between which two whole numbers next to each other does √110 lie?
High School (9–10), General · Rational and Irrational NumbersStemPy LabStemPy Lab
Medium
17.
In the square root spiral, the first triangle has two sides of 1, and each new triangle has one…
High School (9–10), General · Rational and Irrational NumbersStemPy LabStemPy Lab
Medium
18.
Find three rational numbers between 2/5 and 3/5.
High School (9–10), General · Rational and Irrational NumbersStemPy LabStemPy Lab
Medium
19.
Show that √5 is irrational. Why does the same argument fail for √9?
High School (9–10), General · Rational and Irrational NumbersStemPy LabStemPy Lab
Hard
20.
The fraction 355/113 is a famous value for π, far better than 22/7.
High School (9–10), General · Rational and Irrational NumbersStemPy LabStemPy Lab
Medium
21.
Is 0.2022022202222… rational or irrational, if the run of twos grows by one each time?
High School (9–10), General · Rational and Irrational NumbersStemPy LabStemPy Lab
Easy
22.
Which of these fractions have a decimal that ends: 13/32, 7/15, 35/56, 17/125?
High School (9–10), General · Rational and Irrational NumbersStemPy LabStemPy Lab
Medium
23.
Write 0.454545… as a fraction in lowest terms.
High School (9–10), General · Rational and Irrational NumbersStemPy LabStemPy Lab
Medium
24.
Find the repeating block in the decimal of 1/13, and say how many digits it has.
High School (9–10), General · Rational and Irrational NumbersStemPy LabStemPy Lab
Medium
25.
Which of these numbers are rational? -7, 0, 5/11, 0.875, 0.1666…, √36, √12, π/2, 3.1416
High School (9–10), General · Rational and Irrational NumbersStemPy LabStemPy Lab
Easy