Other tags that relate to Peaches in General
Handling data. Place value. Creating and manipulating expressions and formulae. Spreadsheets. Iteration. Mathematical reasoning & proof. Multiplication & division. Mathematical modelling. Generalising. Algorithms. Interactivities.There are 32 results
Broad Topics > Properties of Numbers > Powers & roots
Unusual Long Division - Square Roots Before Calculators
Age 14 to 16
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?
Negative Power
Age 14 to 16
Challenge Level
What does this number mean ? Which order of 1, 2, 3 and 4 makes the highest value ? Which makes the lowest ?
Like Powers
Age 11 to 14
Challenge Level
Investigate $1^n + 19^n + 20^n + 51^n + 57^n + 80^n + 82^n $ and $2^n + 12^n + 31^n + 40^n + 69^n + 71^n + 85^n$ for different values of n.
Enriching Experience
Age 14 to 16
Challenge Level
Find the five distinct digits N, R, I, C and H in the following nomogram
Consecutive Squares
Age 14 to 16
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?
Rationals Between...
Age 14 to 16
Challenge Level
What fractions can you find between the square roots of 65 and 67?
Perfectly Square
Age 14 to 16
Challenge Level
The sums of the squares of three related numbers is also a perfect square - can you explain why?
Cubes Within Cubes
Age 7 to 14
Challenge Level
We start with one yellow cube and build around it to make a 3x3x3 cube with red cubes. Then we build around that red cube with blue cubes and so on. How many cubes of each colour have we used?
Power Mad!
Age 11 to 14
Challenge Level
Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.
Largest Number
Age 11 to 14
Challenge Level
What is the largest number you can make using the three digits 2, 3 and 4 in any way you like, using any operations you like? You can only use each digit once.
Number Rules - OK
Age 14 to 16
Challenge Level
Can you produce convincing arguments that a selection of statements about numbers are true?
Archimedes and Numerical Roots
Age 14 to 16
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?
Roots Near 9
Age 14 to 16 Short
Challenge Level
For how many integers 𝑛 is the difference between √𝑛 and 9 is less than 1?
Lost in Space
Age 14 to 16
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?
Guesswork
Age 14 to 16
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.
Rachel's Problem
Age 14 to 16
Challenge Level
Is it true that $99^n$ has 2n digits and $999^n$ has 3n digits? Investigate!
Surds
Age 14 to 16
Challenge Level
Find the exact values of x, y and a satisfying the following system of equations: 1/(a+1) = a - 1 x + y = 2a x = ay
What an Odd Fact(or)
Age 11 to 14
Challenge Level
Can you show that 1^99 + 2^99 + 3^99 + 4^99 + 5^99 is divisible by 5?
More Magic Potting Sheds
Age 11 to 14
Challenge Level
The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?
Equal Temperament
Age 14 to 16
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.
Root to Poly
Age 14 to 16
Challenge Level
Find the polynomial p(x) with integer coefficients such that one solution of the equation p(x)=0 is $1+\sqrt 2+\sqrt 3$.
Magic Potting Sheds
Age 11 to 14
Challenge Level
Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?
Power Countdown
Age 14 to 16
Challenge Level
In this twist on the well-known Countdown numbers game, use your knowledge of Powers and Roots to make a target.
Fit for Photocopying
Age 14 to 16
Challenge Level
Explore the relationships between different paper sizes.
Deep Roots
Age 14 to 16
Challenge Level
Find integer solutions to: $\sqrt{a+b\sqrt{x}} + \sqrt{c+d.\sqrt{x}}=1$
Power Crazy
Age 11 to 14
Challenge Level
What can you say about the values of n that make $7^n + 3^n$ a multiple of 10? Are there other pairs of integers between 1 and 10 which have similar properties?
NRICH is part of the family of activities in the Millennium Mathematics Project.