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#### Resources tagged with Powers & roots similar to Bus Route:

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Broad Topics > Numbers and the Number System > Powers & roots

### Largest Number

##### Stage: 3 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.

### Like Powers

##### Stage: 3 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.

### Diggits

##### Stage: 3 Challenge Level:

Can you find what the last two digits of the number $4^{1999}$ are?

### Two Many

##### Stage: 3 Challenge Level:

What is the least square number which commences with six two's?

##### Stage: 3 Challenge Level:

Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.

### Magic Potting Sheds

##### Stage: 3 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?

### Enriching Experience

##### Stage: 4 Challenge Level:

Find the five distinct digits N, R, I, C and H in the following nomogram

### Power Crazy

##### Stage: 3 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?

### Lastly - Well

##### Stage: 3 Challenge Level:

What are the last two digits of 2^(2^2003)?

### More Magic Potting Sheds

##### Stage: 3 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?

### Sept 03

##### Stage: 3 Challenge Level:

What is the last digit of the number 1 / 5^903 ?

### 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...

### Napier's Location Arithmetic

##### Stage: 4 Challenge Level:

Have you seen this way of doing multiplication ?

### Rachel's Problem

##### Stage: 4 Challenge Level:

Is it true that $99^n$ has 2n digits and $999^n$ has 3n digits? Investigate!

### 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.

### 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?

### 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 ?

### Double Trouble

##### Stage: 4 Challenge Level:

Simple additions can lead to intriguing results...

### Deep Roots

##### Stage: 4 Challenge Level:

Find integer solutions to: $\sqrt{a+b\sqrt{x}} + \sqrt{c+d.\sqrt{x}}=1$

### Perfectly Square

##### Stage: 4 Challenge Level:

The sums of the squares of three related numbers is also a perfect square - can you explain why?

### 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.

### 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?

### 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 $1+\sqrt 2+\sqrt 3$.

### Sissa's Reward

##### Stage: 3 Challenge Level:

Sissa cleverly asked the King for a reward that sounded quite modest but turned out to be rather large...

### 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.

### 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?

### Rationals Between...

##### Stage: 4 Challenge Level:

What fractions can you find between the square roots of 65 and 67?

### 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.

### The Root of the Problem

##### Stage: 4 and 5 Challenge Level:

Find the sum of this series of surds.

### 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?

### 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!