Resources tagged with Powers & roots similar to Giants:
Other tags that relate to Giants
Manipulating algebraic expressions/formulae. Index notation/Indices. Inequality/inequalities. Comparing and Ordering numbers. Binomial Theorem. Mathematical reasoning & proof. Surds. Modulus arithmetic. Powers & roots. Graphs.There are 38 results
Broad Topics > Numbers and the Number System > Powers & roots
Giants
Stage: 5 Challenge Level: 
Which is the bigger, 9^10 or 10^9 ? Which is the bigger, 99^100 or 100^99 ?
Rachel's Problem
Stage: 4 Challenge Level:
Is it true that $99^n$ has 2n digits and $999^n$ has 3n digits? Investigate!
Rationals Between...
Stage: 4 Challenge Level:
What fractions can you find between the square roots of 65 and 67?
Enriching Experience
Stage: 4 Challenge Level:
Find the five distinct digits N, R, I, C and H in the following nomogram
Staircase
Stage: 5 Challenge Level:
Solving the equation x^3 = 3 is easy but what about solving equations with a 'staircase' of powers?
Negative Power
Stage: 4 Challenge Level:
What does this number mean ? Which order of 1, 2, 3 and 4 makes the highest value ? Which makes the lowest ?
Root to Poly
Stage: 4 Challenge Level:
Find the polynomial p(x) with integer coefficients such that one solution of the equation p(x)=0 is $1+\sqrt 2+\sqrt 3$.
Guesswork
Stage: 4 Challenge Level:
Ask a friend to choose a number between 1 and 63. By identifying which of the six cards contains the number they are thinking of it is easy to tell them what the number is.
Plus or Minus
Stage: 5 Challenge Level:
Make and prove a conjecture about the value of the product of the Fibonacci numbers $F_{n+1}F_{n-1}$.
Perfectly Square
Stage: 4 Challenge Level:
The sums of the squares of three related numbers is also a perfect square - can you explain why?
Consecutive Squares
Stage: 4 Challenge Level:
The squares of any 8 consecutive numbers can be arranged into two sets of four numbers with the same sum. True of false?
Lost in Space
Stage: 4 Challenge Level:
How many ways are there to count 1 - 2 - 3 in the array of triangular numbers? What happens with larger arrays? Can you predict for any size array?
The Root Cause
Stage: 5 Challenge Level:
Prove that if a is a natural number and the square root of a is rational, then it is a square number (an integer n^2 for some integer n.)
Weekly Challenge 34: Googol
Stage: 5 Short Challenge Level:
Find the smallest value for which a particular sequence is greater than a googol.
Ab Surd Ity
Stage: 5 Challenge Level:
Find the value of sqrt(2+sqrt3)-sqrt(2-sqrt3)and then of cuberoot(2+sqrt5)+cuberoot(2-sqrt5).
Archimedes Numerical Roots
Stage: 5 Challenge Level:
How did Archimedes calculate the lengths of the sides of the polygons which needed him to be able to calculate square roots?
Unusual Long Division - Square Roots Before Calculators
Stage: 4 Challenge Level:
However did we manage before calculators? Is there an efficient way to do a square root if you have to do the work yourself?
Smith and Jones
Stage: 4 Challenge Level:
Mr Smith and Mr Jones are two maths teachers. By asking questions, the answers to which may be right or wrong, Mr Jones is able to find the number of the house Mr Smith lives in... Or not!
Archimedes and Numerical Roots
Stage: 4 Challenge Level:
The problem is how did Archimedes calculate the lengths of the sides of the polygons which needed him to be able to calculate square roots?
Em'power'ed
Stage: 5 Challenge Level:
Find the smallest numbers a, b, and c such that: a^2 = 2b^3 = 3c^5 What can you say about other solutions to this problem?
Rational Roots
Stage: 5 Challenge Level:
Given that a, b and c are natural numbers show that if sqrt a+sqrt b is rational then it is a natural number. Extend this to 3 variables.
Equal Temperament
Stage: 4 Challenge Level:
The scale on a piano does something clever : the ratio (interval) between any adjacent points on the scale is equal. If you play any note, twelve points higher will be exactly an octave on.
Number Rules - OK
Stage: 4 Challenge Level:
Can you convince me of each of the following: If a square number is multiplied by a square number the product is ALWAYS a square number...
Square Pair Circles
Stage: 5 Challenge Level:
Investigate the number of points with integer coordinates on circles with centres at the origin for which the square of the radius is a power of 5.
Function Pyramids
Stage: 5 Challenge Level:
A function pyramid is a structure where each entry in the pyramid is determined by the two entries below it. Can you figure out how the pyramid is generated?
Fit for Photocopying
Stage: 4 Challenge Level:
Explore the relationships between different paper sizes.
Power Countdown
Stage: 4 Challenge Level:
In this twist on the well-known Countdown numbers game, use your knowledge of Powers and Roots to make a target.
Route to Root
Stage: 5 Challenge Level:
A sequence of numbers x1, x2, x3, ... starts with x1 = 2, and, if you know any term xn, you can find the next term xn+1 using the formula: xn+1 = (xn + 3/xn)/2 . Calculate the first six terms of this. . . .
Take a Square
Stage: 4 Challenge Level:
Cut off three right angled isosceles triangles to produce a pentagon. With two lines, cut the pentagon into three parts which can be rearranged into another square.
Deep Roots
Stage: 4 Challenge Level:
Find integer solutions to: $\sqrt{a+b\sqrt{x}} + \sqrt{c+d.\sqrt{x}}=1$
Fibonacci Fashion
Stage: 5 Challenge Level:
What have Fibonacci numbers to do with solutions of the quadratic equation x^2 - x - 1 = 0 ?
Pythagorean Fibs
Stage: 5 Challenge Level:
What have Fibonacci numbers got to do with Pythagorean triples?
Napier's Location Arithmetic
Stage: 4 Challenge Level:
Have you seen this way of doing multiplication ?
NRICH is part of the family of activities in the Millennium Mathematics Project.