Finding Roots of Numbers
Read this topicExplanations 4
- Finding Roots Most roots of larger numbers can be broken into smaller roots. It is a good idea to memorize the smaller squares. xx2243941652563674986498110100xx32832746451256216…
By Ben Ferrara, Alex Federspiel, Amy Feraco, Jonathan Heller
- Example Walk-through \\ We have established that we can convert between rational exponents and radicals. When finding the root, we cannot always find a nice whole number. Recall…
By Christine, Eunji Kwon, Victor Wang, Alex Federspiel
- Strategy to Finding Roots and Simplifying \\ Finding the root of perfect squares and cubes rely on some familiarity with numbers. For example, we immediately know the square roo…
By Christine, Alex Federspiel, Amy Feraco
- (Video) Finding real number roots by T Demott In this video, we take a look at finding real roots. Summary\large{\text{Summary}}Summary We see the prime factorization of −83\sqr…
By Amy Feraco
Problems 26
- Find the largest integer nnn for which n200<5300n^{200} < 5^{300}n200<5300. Source: Alex Zhu, Problems of the Week 2, 2012
- What is the cubed root of 125125125?
- What is 81\sqrt{81}81?
- What is 72737\sqrt[3]{27}7327?
- What is 8−838\sqrt[3]{-8}83−8?
- What is 777 times the square root of 494949?
- The graph y=f(x)y = f(x)y=f(x) of a function f(x)=logb(x)f(x) = \log_b(x)f(x)=logb(x) passes through the point (9,2)(9,2)(9,2). (Here b>1b>1b>1.) Find bbb.
- A colony of bunny rabbits grows exponentially. Suppose that in 201220122012, there are 400400400 bunny rabbits, and in 201620162016, there are 640064006400 bunny rabbits. How ma…
- There were approximately 333 billion people on Earth in 196019601960, and approximately 666 billion people on Earth in 199919991999. Assuming that the population growth is expon…
- If 72y=367^{2y} = 3672y=36, compute 7−y7^{-y}7−y. Write your answer as a fraction pq\frac{p}{q}qp in simplest form, with no spaces.
- Evaluate 4\sqrt{4}4.
- Evaluate 16\sqrt{16}16.
- Evaluate 64\sqrt{64}64.
- Evaluate 9\sqrt{9}9.
- Evaluate 81\sqrt{81}81.
- Evaluate 196\sqrt{196}196.
- Evaluate 225\sqrt{225}225.
- Evaluate 400\sqrt{400}400.
- Use intuition, previous information, and math tricks to help evaluate the following root, WITHOUT a calculator. 100040004\sqrt{100040004}100040004
- Simplify 256\sqrt{256}256.
- Evaluate 28\sqrt{28}28.
- Solve the following equation for the positive value of xxx: x2=81x^{2} = 81x2=81
- Solve the following equation for the positive value of xxx: x2=625x^{2}=625x2=625
- Evaluate 14400\sqrt{14400}14400.
- If Jeremy had as many sets of apples as he had apples, he would have 144144144 apples. How many apples does Jeremy have?
- Evaluate 361\sqrt{361}361.